There are three main ways that leagues are run. There's rotisserie, points-based and head-to-head.
In a rotisserie system, a league decides on a set number of statistics that are used (typically 8 to 12, sometimes less, sometimes more) and then owners are ranked in that statistic every week. For example, let's say it's a 10-team league and your stats are home runs, runs batted in, team batting average and team stolen bases for hitting, and team ERA, total wins, total saves and WHIP (walks plus hits divided by innings pitched) for pitching. Those are some of the most common stats, although essentially any statistic can be used.
In a rotisserie format, the owners' players are then ranked in every statistic, with 10 points for the most home runs, 9 for the next, etc. And the player with the most points wins the week, or the season, etc.
In a points-based system, players receive a set number of points based on a format the league decides. Maybe four points for a home run, three for a triple, one for a single 10 for a pitching win, etc. And then those points are added up, and the owner with the most points wins.
In a head-to-head league either format could be used, but a twist is added by creating a schedule of player vs. player. An owner then competes solely against another owner for a set period of time (usually a week), and the winner gets a win or loss. Standings and divisions are set up, and the owner with the best record can win a league or make the playoffs, just as in a real sports league.

