The strong safety lines up on the strong side - whichever side of the center has the most lineman on it (typically the tight end is the extra guy). If both sides have an equal amount of lineman (maybe a tight end on both sides of the line) the strong safety will typically line up across from whichever tight end they want to shut down in the passing game or whichever side they believe the run is going to go to.
Strong safety refers to the fact that the safety in that position is playing on the strong side of the field. Just like a strongside linebacker, the strong side of the field in man coverage is the side of the field where there are more lineman and where a play is designed to be run. A typical indicator is where the tight end lines up.
In man coverage, the strong safety has the obligation of covering the tight end down the field AND coming up to provide run support. In a man formation, he will typically line up closer to the line of scrimmage so he can pick up the tight end quicker as the tight end runs by the strongside linebacker, who is the first line of defense on the strong side.
Like the strongside linebacker, the strong safety is normally a bigger safety who is fast enough to make up ground in the pass game, but who can take on tight ends and fullbacks to make a tackle on the running back in the running game. The strong safety has to be a big hitter, has to be tough, and has to be good at shedding blockers and taking the correct angle to get to the runner the quickest. He's often the safety that will blitz the quarterback on a third down as an overload on either side of the formation.
The free safety position is much different than the strong safety position. With strong safety, you really need a particular style of player who is rugged and rough. Free safety the player normally needs to be great at coverage and understanding the angles to get to the ball. It helps if he's taller and leaner and is a great jumper as well. He can't be afraid to make a big hit, but also must time his hit the right way to jar the ball loose and not get a penalty. He is the guy that makes the wide receivers scared to go over the middle.
He's also the guy tasked with locating the ball and meeting it at the point of attack, whether that point is an interception, deflection, or that big hit.
He's tasked with "playing the field" and assisting the cornerbacks and he often plays zone when others around him are playing man. When he does play man defense, it's often because there may be a blitz package or a run style defense (like a 4-4) they are in. At that point, he has the duties of a corner in coming up more to pick up a wideout. The weakside linebacker will normally act as the strongside linebacker does with the tight end and drop with the WR for a few yards until the free safety picks him up.