IMPs, Matchpoints, Total Score, Pairs, Individual, Goulash, Speedball, Slowball, Inbetweenball, or any combination of these, you can usually find a tournament to your liking starting soon on BBO.
You should know that the rules for tournaments can vary widely among the organizations or tournament directors holding these games for you. Because psychic bids are forbidden in one tournament doesn't mean you can't psych in another. This means it's important for you to carefully read the rules in the tournament description before joining a tournament to see what is or is not allowed in that particular game. If you disagree with the rules for a tournament, don't join it.
Some tournaments are free, others have an entry fee. An entry fee tournament is clearly shown by the $ sign under the Register heading you'll see on the line describing that game.
In order to join a tournament that has an entry fee, you need to have a BB$ account. You can read about how to do this in the BB$ help file in the Basics help section, or just click on the BB$ button at the top of your screen to start your account.
You may, from time to time, disagree with a ruling by a tournament director in a particular game. Each organization holding tournaments on BBO are responsible for what goes on in their games. So if you disagree with a ruling in a game, want information on a prize won, or anything else to do with a completed tournament, you would contact that organization directly. You can find the contacts for each organization or club in the help file section Bits and Pieces under Club Contacts.