It goes something like this:
Set format (In Order of Procedure):
1. Opponents choose their characters for the first match *
2. Opponents start the stage striking procedure
(You start off with a set of starter stages and you and you opponent take turns eliminating them them until you get to one)
3. Each player may announce one stage to be banned for counterpicks of the set
(You can eliminate one stage you dislike for every game you play with that opponent)
4. The first game is played, using the stage chosen during step 2
5. The loser of the previous match announces the next match's stage from either the Starter Stage List or the Counter Stage List
(Basically, you choose a stage you think you'd do well on)
6. The winner of the previous match chooses their character
7. The loser of the previous match chooses their character
8. Repeat steps 5-7 for all proceeding matches
*Double blind character selection may be called for the first match
And that's it in laymen terms. It's from the rules linked
here.
