To play golf, the first thing you need is a set of clubs. I will echo iandotkelly; used clubs are the beginner's best friend. People get rid of clubs all the time, either because they bought new ones or because they've had enough and are giving up the game. Look for local garage sales, check bulletin boards at local public courses, take a look at the 'List or the 'Bay, and check the "pre-owned" racks at local golf stores (Golfsmith deals heavily in used clubs from trade-ins at local stores). Judging by what I've seen, you should be able to put together a good set of clubs with bag for about $300 if you buy used clubs from a retailer. If you luck out at a garage sale or Craigslist listing, you could walk away with a full set of nice clubs for $25-$50 if the guy just wants to be rid of them. Contrasting that, buying a full set in a bag from a reputable brand like Adams or Macgregor will start at $500, and buying new components separately (driver, woods, iron set, wedges and putter) can easily run you over a grand. Don't do that until you know what you want in a set of clubs to fit your game (and are rich/interested enough to justify it).
When assembling your clubs, the minimum you will want is a driver, 3-wood, a numbered iron set (typically from 3 or 4 through pitching wedge), a sand wedge and a putter. That's 11 to 12 clubs and will allow you to play from pretty much any lie. Once you identify the types of clubs you use best, or situations in which you don't have a good club for the job, you can add two or three clubs and look at replacing clubs in order to play to your strengths or fill in the gaps. Common additions are a 5-wood, for fairway shots where you'd normally use a hard-to-hit long iron; hybrids to replace long irons; and additional wedges to dial in the right distance in your short game.
Things to look for in your first set of clubs:
Cavity-back irons. These irons will remove material from the middle of the clubhead, and instead place most of it low and rearward, and the rest around the perimeter of the clubhead. This design is favored by the casual player because it is more forgiving of slight mis-hits (it can be said to have a larger "sweet spot"). Ten to fifteen years ago, these designs were brand new and the used market was full of the older, less forgiving "muscle-back" designs as golfers traded up. Now, these cavity designs are plentiful in the secondhand market, and honestly, this was the last real quantum leap in clubhead design, so you won't lose much technology-wise going used.
Regular flex on graphite shafts. The used market is littered with clubs bought by people who thought the club made the golfer, and so went for stiff-shaft, 9.5*-loft drivers because that's the club their favorite tour pro uses, then got rid of it because they could only hit 200-yard worm-burners. The majority of golfers will get the best performance out of a 10.5*, regular-flex driver configuration, and regular flexes on any other graphite shafts in their club set (virtually all woods have graphite shafts; they're also common on hybrids. Graphite vs steel on the long irons is a personal preference, but virtually all short irons and wedges are steel-shafted for consistency). These configurations, because they do work well for the average golfer, are rarer than the outliers on used racks, but you can usually find a few good candidates.
A slight draw bias on the driver. Again, a lot of players want the best and so they buy a driver labelled "tour" because they think they're getting the best quality. What they don't realize is that a Tour driver has either no bias, or a slight fade bias to correct for clubhead torquing with their stronger swing. In the hands of a casual golfer, a driver like this will probably push-slice uncontrollably. Most golfers, again, benefit from using a "game improvement" driver (typically marketed as just a regular driver), which has a slight 1-2* bias toward closing the face of the club, to compensate for the natural tendency to open the clubface when you just "grip it and rip it". However, avoid "max game improvement" or "draw" drivers; these have an extreme draw bias, up to 5* towards closed, and are intended for people who just can't stop slicing their driver and are unable or unwilling to change their swing. Learn how to swing a "regular" driver straight, and you'll minimize bad habits.
A good putter. If there's one club that you should buy new for your first set, it's your putter. The pros drive for show, but putt for dough; putting is a high-precision, high-finesse aspect of golf, and it's where you make or break pars and birdies. So, you'll want a putter that feels good in your hands, that you can swing with the proper tempo and in line. Good, late-model used putters don't tend to hit the racks as often as other clubs (players will take their time looking for the right putter, and will stick with it for a very long time), and when they do they're snapped up quickly, but keep an eye out. There are dozens of designs of putter, all varying subtly in weight distribution, hosel/shaft positioning, visual cues, etc which can make one putter better than another for you. Learning to putt well is frustrating as it is; the last thing you want to do is have to compensate for a putter that feels "wrong", or is out of alignment. Any inaccuracy in putting should be all you, so you know what to fix.
You will likely also want a glove for your "leading hand"; whichever hand is closer to the butt end of the grip (for a right-hander this will be your left hand). This glove will allow you to get a better grip on the club and will avoid blisters.
Lastly, you'll want comfortable clothing that doesn't restrict movement. Golf attire is traditionally unfashionable, and even modern stuff can sometimes be a little out there, but there's good stuff too; while you can buy specialized clothing, all you really need is a polo shirt and a pair of casual-wear khaki shorts or slacks (not dress slacks) that fit you well and allow free range of motion. A lot of brands are touting "moisture-wicking synthetics" for athletic wear that breathe well and keep you dry, but I know plenty of players that swear by a good ol' 100% cotton polo. Your choice; down here in Texas, hot is hot, and color is more important than fabric.
Once you have the equipment, you'll probably want a lesson. Check your local driving ranges for a "group lesson", or if you have some money to spend, get a private lesson. If you have absolutely zero money, or just want to try learning yourself, there are many online resources from Youtube vids to blog posts about everything having to do with the golf swing. As much as the pros say it's an easy, natural movement, the golf swing is a very complex motion, and as golf is a precision sport, small changes can have big impacts. Having a coach look at your own individual swing and correct the things you're doing wrong will help you, but you may just want to go out and hit a bucket before calling in the coach, so you can get a feel for your new clubs.
Before you hit the links, you should be able to hit every club in your bag straight enough that people on the path won't be cowering behind their carts, and consistently enough that you can predict where it will fly and compensate for any inherent push, pull, draw or fade in the flight path of your ball. You should also be making good contact with the ball with every swing (no whiffs, tops, thin or fat shots). This will allow you to put the ball where you want it on the course and avoid the 20-yard walk of shame from the tee box after topping your drive.
And don't forget your putter; remember that par is based on 2 putts, for good reason, and so for a typical par-72 course, fully half of those strokes will be putts if you know what you're doing. Lots of driving ranges and courses have chipping and putting greens, but you may have to pay more to use them. A game or three of miniature golf can help with getting a good putting line, but it can also hurt; miniature golf uses artificial turf and artificial terrain slopes, which generally make for "fast" putts and relatively easy-to-read shots; a real putting green will have less even grass, a "grain" inherent in the way the grass grows, and a slope (and natural variations thereof) to its surface which will make putts break, and a good short-game player must learn to read these elements and adjust their putting line.
If you watch the pros play, you'll notice their secret; putt with exactly the strength needed to get to the hole, so that if you don't put it in the hole it's right there for the tap-in instead of a "knee-knocker" (close enough that you're expected to hole it, but far enough to miss). Practice doing this; putt towards the hole from varying distances, and work on getting the ball within a foot of the cup (if it goes in from 10 feet, great; if it doesn't you have an easy second putt). There are many techniques for getting the proper putting power; the two most common are a pendulum swing (vary the backswing by the amount of power you need, and then simply relax and let the putter fall through the arc) and a "power putt" (take a short backswing, then add the proper power from your trailing hand into and through the ball). These both take a lot of practice.
You will also want the following for a round of 18 holes of real golf:
- Realistic expectations - Even if you hit relatively consistently and accurately at the range, you should not expect to par every hole, or even to bogey every hole. My very first round was a 116, and we weren't counting most of the penalty strokes I should have gotten. First-timer strict-rules scores of over 200 are not unheard of (though most casual players will stop counting by strict rules after the third quintuple-bogey in a row). On a real course, the ground is uneven, the grass is of varying length, the ground is harder and softer, your surroundings and visual cues will change with every shot, you'll have to accurately judge distances without the aid of those flags and signs out on the range (depending on the course you may not even be able to see the pin from your approach shot), and there's water, sand, leaves, stones, trees, bushes, high grass, and all manner of other things that will make pretty much every shot (including tee shots) less than ideal. You WILL score terribly your first time out no matter how you're counting. If you don't like the score, don't turn in the card.
- A sense of humor - As Leslie Nielsen said, the reason they call it "golf" is because all the other four-letter words were taken. This goes right along with the previous point; you WILL whiff a tee shot or two, you WILL watch a tee or fairway wood shot soar off to the right into somebody's backyard, you WILL pop the ball straight up in a sand trap and watch it plop right back down, and in general you WILL make shots you'd rather forget. Better to laugh them off with the rest of your group than to get frustrated and make more bad shots.
- A knowledge of the rules of golf - Not just the rules, but the traditional etiquette. These rules are available in PDF format for free at http://www.usga.com, or you should be able to buy the paperback version from any golf retailer with a book section, or bookstore with a sports section. The rulebook will include a summary digest towards the front, which you should read every word of; it contains the rules and situations that the average player will need to know, in a format that's easier to read than the strict rules later on.
- Knowledge of any additional local rules and dress code at the course you will play - In addition to the "strict rules", many courses have their own additional "local rules", covering specific things that differ from course to course and day to day. These rules are usually put in place to help preserve the course from damage, avoid injuries, speed up play, or address things that are relatively unique to this course, such as how various boundaries are marked. In addition, country clubs and even many public courses enforce a minimum dress code, and depending on how specific it is the clothes you bought for the range may not meet it. Better to know up front that all players must wear a white collared short-sleeve shirt and khaki shorts, than to show up in a t-shirt and jeans on the day and miss your tee time because you had to go back home and change (or buy radically marked-up clothing from the pro shop).
- A friend or three to play with - While playing solo speeds up the pace (when you know what you're doing) and avoids the embarassment of a witness to your bad shots, IMO golf is best played with others of similar skill, maybe with one "ringer"; you'll give as good as you get on the embarassment front, you'll have witnesses to your better shots, and your playing partners will keep you honest (and help you find that sliced tee shot, or the one that bounced off that tree...).
- Plenty of golf balls - Like I said, you're not going to par every hole, and so you are most likely not going to find every ball after you hit it. I've used over 25 balls to play one round of golf (do the math; that's losing about 1.5 balls per hole played). For that reason, there's not much sense for me to buy new. There are "recycled" balls available under a couple of brand names, MUCH cheaper than new top-quality balls. The most expensive recycled ball sold by Reload, a top-graded Titleist Pro V1, is $18 for a dozen; the same dozen balls brand new would cost you $50. For about the same $20 price, you can get a bag of 48 "shags" (more weathered, more blemishes, lesser-name brands and lower technology levels) which are perfect for casual play as well as backyard chipping. Losing a ball that cost you 50 cents is much better than losing one that cost you $5, especially when you're losing a lot.
- Tees - Pick up a bag of the ordinary wooden deep (3 1/4") tees to use with your driver. For irons and fairway woods, you typically want these set up just a hair above the turf level anyway (as that's how you normally hit them on the rest of the course), and for that there's a little trick; find or save the top of a broken tee and use that instead of buying a bag of shorter tees. Don't worry too much about buying more expensive tees for now (not all of the more expensive designs are gimmicks, but you'll need to know through experience how a tee might help you), and don't worry about losing or breaking these wooden ones; you'll pay $5 for 100, and that'll last you many rounds.
- A hat, sunglasses, and sunscreen - You will be outside in the sun for up to four hours, after all, and unless you start very late you'll be out during the middle of the day when the sun is hottest and the air is thinnest. A ballcap is usually acceptable (check the dress code; a different style of hat may be required), and if you burn easily, slather yourself with SPF45 sunscreen and keep it handy. Sunglasses reduce glare (remember you'll have water hazards on most courses that will reflect the sunlight) and are generally a good idea overall to protect your eyes; my grandfather-in-law was an avid golfer and now suffers from macular degeneration caused by long-term overexposure to light.
- Bug repellent - Thanks to gbianchi for the reminder. On top of your sunscreen, a shot of Deep Woods Off helps keep the little biters away. Not only are they an annoyance while you're concentrating on that putt for birdie, but they carry a host of diseases from West Nile to Lyme disease to malaria (depending on the region) that you really don't want to get. You'll also likely be traipsing through tall grass looking for an errant shot, and the bug repellent will also keep ticks and chiggers off of you.
- Golf shoes - While tennis shoes are OK for the level, artificial turf of the driving range, golf cleats are designed to allow you to pivot on your feet but prevent sliding sideways; this will become invaluable the first time you hit the ball into a sand trap or into marshy ground. While stereotypically tacky, like the clothing, modern golf shoes are available in many styles including those similar to tennis shoes or cross-trainers. Courses may require shoes designed for golf (banning tennis shoes, loafers, athletic cleats etc) and/or may specify the type of cleat spikes that are allowed (typically metal spikes are banned, whether they're on proper golf shoes or some other athletic shoe like baseball cleats).
- A divot tool - When you hit onto the green, the ball will often make a dent on the putting surface. It's good etiquette to fix these so other golfers have a nice level putting surface to play on. A divot tool is a two-tined fork, and you stick it into the ground around the divot and push inward to lift the divot, then smooth it back out with something flat (strict rules say you can't touch the green with your hands; you typically use the bottom of your putter).
- Ball markers - These are used to mark your ball's position whenever you have to pick it up (commonly on the green). Many players will just use a penny or dime; others will have more personalized markers that are available from golf stores. Many other items sold for use on the course often have ball markers integrated; divot tools, carrying cases for tees, etc.
- A stroke counter - Optional, but handy if you're expected to keep an accurate score (remember, by strict rules recording a lower score than you actually shot will disqualify you). The simplest are just thumbwheels, clickers or strings of beads, and they're very inexpensive.
- A towel and/or stiff brush - to clean hands, clubs, balls, etc. All of these will get wet, muddy, sandy etc through a round. Remember there are certain situations where you can, and cannot, clean your ball.