I've never considered myself an autograph seeker, but at last night's Braves game, my girlfriend and I had this adventure. The way it works (at least at Turner Field, though I suspect that it's similar at all parks) is that the teams each take their batting practice, usually home team for half an hour and then away team for half an hour, and then there's a break before gametime. If you get to the park early enough, you can move down to the dugout area and try to get players to sign things for you. Now this was an interesting process. Some fans were rude, and some players were rude. Most players just seemed too busy. I can understand why some of them wouldn't want to sign - these days, people are looking to make money, instead of collecting for the pure joy of it. Some of these guys had bags full of balls, jerseys, cards, etc and they were insane in their methods and expectations. Still, it was interesting to watch the process, even if (like me) you were just standing there without anything to get signed.
In any case, after a failed attempt, the outlook was bleak...but then she got aggressive, and perhaps lucky, and ended up with her Nomar Garciaparra jersey personally signed by the man himself, made out to her. It was a dream come true, for a kid of any age.