I am an assistant fencing coach for a collegiate club.
Several injury risks I've encountered:
Poked in the eye/face/chest/"below the belt"/etc: This is most common. Being accidentally poked in some places are less severe than others, but it is still a common risk. In addition, the tip at the end of your fencing weapon may be loose or missing. A weapon without a tip is more painful than with one.
Twisted ankles (ligament tears are less common, but possible): In some fencing positions, one is susceptible to twisted ankles/ligament tears simply by shifting your weight the wrong way. An example: After a lunge, you can twist your ankle causing the rest of that side of your lower body to collapse. A member actually suffered ligament tears in her knee when I was a student, and was in a full leg brace for about a year.
To prevent these risks:
Safety first. Use common sense. Don't put yourself or others in risk.
Take time to learn the fundamentals. Many people are interested in fencing because it "looks cool," but these same people lose interest because they are not willing to put forth effort to learn the fundamentals. In my club, if you think you're going to use a weapon during your first month of drills, think again. It is not a toy.
When fencing, wear appropriate fencing gear. This includes:
Mask
Glove
Jacket
Underarm protector (plasteron)
Chest protector (mandatory for females; optional for males)
Knickers
Knee-length socks
Fencing/tennis or court shoes
My club only requires socks, sneakers, and appropriate attire (t-shirt, gym shorts) for warm-ups, conditioning, and drills. When a weapon is involved, we require most of the gear listed above. We are lenient about the underarm protector, knickers, and knee-length socks.....but we are stringent about the rest, especially a mask.
NOTE: Even if you're horsing around or fencing lightly, wear gear. Accidents are most common when we are not at an appropriate awareness level. That, compounded with not wearing gear, can result in a costly accident that could have been easily prevented.
- Scan your equipment before use. Make sure the equipment you are using is in good, maintained condition. As I state above, a weapon without a tip is more painful than with one. This can be easily prevented if you take a careful look over your equipment before you use it. If something doesn't look right, let someone (who knows what they are doing) know.
Hope this helps, and hope I didn't scare you and your friend away ;)