Baisicly, teams of 2 (You get to choose, of course) against others. It's simple: One member from each team plays another from another team that will be choosen by random. Once one of them loses, then the other from the team that lost faces the same one until one of them has been beaten. If the losing team wins, then he/she plays against the other person.
Player 1 vs Player A - Player A wins
Player 2 vs Player A - Player 2 wins
Player 2 vs Player B - Player 2 wins
Players 1 & 2 win that match
Here's the thing, though. say Player A won with 1000 LP remaining. When he faces Player 2, Player A has to start out with 1000 LP. If you win, you keep the LP you had until you've been beaten or win and advance to the next round.