They go a little something like this, from the finals of last year's rule page (
link):
Stage & Character Selection
1. The higher seed has first choice for their seat(s) and controller port(s). The higher seeded team has first choice for their team color. Teams must sit together on one side or the other. If players/teams meet for a 2nd time in a specific bracket, the winner of the 1st series will have seat and controller choice.
2. The stage for Game 1 will be selected at random unless both players/teams can agree on a stage. After the stage has been randomly selected each player/team may call for a reset. Each player/team can only call for a reset once during a series. If a reset is called, another stage must be randomly selected. The stage that was first selected can't be randomly selected again, but is still available for a counter pick.
3. Singles random select stages: Final Destination, Battlefield, Yoshi's Story, Fountain of Dreams, Dreamland 64 & Pokemon Stadium
4. Doubles random select stages: Final Destination, Battlefield, Yoshi's Story, Rainbow Cruise, Dreamland 64 & Pokemon Stadium, DK64
5. Stages not listed on the random select list that are not banned are open for counter picks by the losing player.
6. Stages banned for Singles Only: Great Bay and Mushroom Kingdom 2
7. Stages banned for Doubles Only: Fountain of Dreams and Mute City
8. Stages banned for Singles & Doubles: Yoshi's Island (Pipes), Fourside, Hyrule Temple, Flatzone, Brinstar Depths, Icicle Mountain, Big Blue, Mushroom Kingdom 1, Venom, Yoshi's Island 64, Peach's Castle, and Kongo Jungle, Onett.
9. No stage may be used twice in a Best of 3 or Best of 5 Series. The random select stages are the only stages that may be used more than once in a Best of 9 or Best of 11 series.
10. After characters have been selected for the first game, each player/team may choose to knock out one stage. Stages that are knocked out won't be used during the series. Random select stages can't be knocked out. The lower seeded player/team must make their knockout selection first. Once the first game has started, stages can't be knocked out.
11. After each game of a series, the player who lost the previous game may choose the stage for the next game or elect for it to be chosen randomly. After the stage has been selected, the winner of the previous game may change characters. After the winner has chosen their character, the loser of the previous game may change characters.
12. For the first game of a series, a player may call for a double-blind pick. This means that all participating players must tell a judge the character they will use for that game. Each player is required to use that character in the game.
13. If players/teams meet for a 2nd time in their respective Open bracket and they played a Best of 3 in the Winners Bracket, their series will expand to a best of 7, include the previous series, and pick up where that series left off. For example, if Team A beat Team B 2 games to 0 in the Winners Bracket, the Best of 7 will resume with Game 3 and Team A leading 2 games to 0. The loser of the 1st series will choose the stage for the 1st game of the 2nd series.
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So it goes a little something like this: People choose the level they want to ban for the set, and then pick their characters
(if necessary, both telling who they want to a tournament director then picking if they each want the other to pick first), and then select 'random stage'.
After that, the loser first gets to pick the stage he wants to counter-pick, which has to not be banned, and not have been played in that set. Then the winner decides the character he wants to play, and the loser then gets to decide what character he wants to play. This repeats until the set is over.
You can also find a picture of stages that are on random/ counter-pickable / banned
here.
