Greebo is right. You join a league for whatever sport is in season. Typically you do this with a bunch of people that you know, but there are ones you can join at random. Then, they have the draft. If it's a bunch of people that know each other, you'll typically have a live draft, where you get together to drink beer, and you take turns going around the room and selecting available players for your team. The order you do this in is usually determined by drawing numbers out of a hat. The number of players you get on the team varies by sport, so since I do Fantasy Football, I'll use that as an example. We get either 15 or 17 players on our team (I can't remember). Then, before the games each week, you can modify your lineup. The positions you can play at a time are determined by your league commissioner. In my league, we could have 1 QB, 3 WR's, 2 RB's, 2 TE's, 1 Kicker, and 1 Defense (you counted an entire team's defense as 1 player). I might be missing a couple, but that's the gist of it.
Then, each stat that the players can put up in their real-live games is assigned a point value before the league starts by the commissioner. I.e., a touchdown is 6 League Points (LP), an extra point attempt is 1 LP, a field goal from 10-30 yds = 3LP, 30-40 yds = 4LP, 10 passing yards = 1 LP, 10 receiving yards = 1 LP, 10 rushing yards = 2LP, etc.
When the league begins, your Fantasy Team will be matched up against another fantasy team from your league each week. After all of your players plays their real-life games, the point values from their stats are added up, and the fantasy team with the most LP's at the end of the game wins. Typically, the fantasy league runs 14 - 15 weeks, depending on the size, then there are 1-2 weeks of playoffs and a championship game. The championship fantasy game always coincides with the last week of the NFL season, since not all of your fantasy players will be on teams that will make it to the real-life playoffs.
There are a few more details, but that's the basic gist of it. There are several online services that provide the stat tracking and league hosting - some for free, some for fee. For my office league, we use Yahoo! Sports.
So, is anyone interested in participating in a POA Fantasy Football League this year? I'd be willing to act as commissioner...