GenCon only refers to the big con in WI; it's a proper name, not a generic name.
Cons will vary. Many have no Q&A panels, but do have lots of games. There will be individual games that people are running themselves, LARPS (liva action games), RPGA-organized games where you are given a character, and RPGA-organized games where you bring your own PC that matches their rules. Some cons have anime rooms, card games, a dealer room, board games, miniatures games, and other features. People will probably be playing D&D along with lots of other game systems; 3e will be most prevalent.
There will be 3-4 "slots" per day when games run. You typically preregister for these or buy a ticket on-site. Cons usually cost about $5-$10 a day, plus $1-$3 per four-hour game.
I recommend you try other games than 3e. A con is the perfect place to do so; you play for 4 hours, then decide whether or n ot you had enough fun to buy it!