Most clubs will let you learn as you go by joining the club and then the team. Best to join the club first and then ask who heads up their program...If your near Taunton, turn green and give me a PM and I'll hook you up...
To spell things out a little more:
The most common 22LR competition is the gallery course of NRA Conventional Pistol, aka "bullseye". This is shot typically at 50 feet and consists of 3 stages, slow fire: 10 shots in 10 min, timed fire: two strings of 5 shots in 20 sec, rapid fire: two strings of 5 shots in 10 sec, all on standard bullseye targets. There are a number of leagues, and most gun clubs with an indoor range field a team in one or more leagues. Typically you shoot 1 night a week and have home and away matches against the various teams in your league.
For example, I shoot for Westford in the Nashoba Valley Pistol League, which consists of: Westford (2 teams), Littleton (2 teams), Tyngsboro, Concord (2 teams), Maynard, Stony Brook, and Musketaquid. We have one home and away match against each team in the league, for an 18 match season running Wednesday nights from October - March.
If you're already a member of a club, check and see if they have a bullseye team.