different regions do stage selection/counterpicking differently.
a common way (the west coast way) is advanced slob picks with stage striking. here's how it works
1. players select characters (double blind pick if someone asks for it, this rarely happens)
2. random stage select is hit of the 6 neutral stages, now either player has the opportunity strike the stage selected by pressing L+R+A+Start. you can reset the selected stage while its loading, or by pressing pause right when the match starts, and reseting it there. each player can strike a random stage ONCE. but if that stage comes up again during the random select, it will not be played.
3. after the match is over, the winner announces a stage ban. once that stage is banned it cannot be played for the rest of the set (common examples: peach players banning corneria against fox, pikachu players banning FD against sheik)
4. after the ban is announced, the losing player announces his counterpick stage. this can be any of the 6 neutral stages plus any of the legal counterpick stages.
5. now that the next stage is announced, the winning player has the opportunity to switch characters. (example: the losing peach picks mute city against the sheik he just lost to, now the sheik can switch to another character like c. falcon if he wants)
6. now, the stage is announced and the winner has had the opportunity to change characters, now the losing player has the opportunity to change characters, then you can play the match.