League play is the place to hone your skills in a team environment, meet new people, and get some exercise to boot. There are leagues in all seasons for all levels of players
Pickup is open, drop-in play. Bring yourself, your cleats, and a light and dark shirt. Pickup games span a very wide range of skills and are usually welcoming of newcomers. If you're looking to find out what the game is all about, pickup is where most players start.
Tournament are a great way to play against tougher competition. Succesfully tournament play requires endurance, skill, savvy and plain-old fashioned hard work. On the other hand, tournaments are alot of fun, and a welcome change up from the regular crowd at pickup or league.
Most local universities have some amount of ultimate being played, and many High Schools and Middle Schools have club or varsity teams on which to participate.