To get a football players autograph the obviousfirst step is you must have something to sign. Having a football player sign your arm may seem like a fun idea at the time--and they may well oblige-but it's largely a pointless act since you're going to eventually wash it off. A good rule of thumb is if you're not going straight to the tattoo parlor to have a tattoo artist trace the autograph, don't bother with body signing. Always carry a good quality pen. What's the point in handing the player something to sign if you don't have something to sign it with?
Next, know who you're talking to. If you can call the player by name, or say something that shows you have taken an interest in him, he's going to look at you more sympathetically than someone else. The next important thing is location, location, location. It is far easier to get a player to sign something from front row seats than from seats in the second balcony.
If you get a good seat and get to the game early, you can also talk to the football players as they walk by. If you can get a player in conversation for a while, you might end up getting a few other players to stop by as well. Sometimes a player will start signing autographs and a crowd will quickly form, which is another reason to get to the game early.
If you can learn where the players come into and out of the stadium, that's another great place to find them ready to sign, pose for photos, shake hands, etc. They're far more likely to stick around for a while when they're not in a hurry.
If you're just looking for a signed photo, you can write the player in care of the team's address. A better way is to also to send an unsigned 8x10 photo iand a self-addressed stamped envelope to the football player's personal address.