How I always did it in Melee:
Both people and come to an agreement on who chooses a character first. Then the other person picks. (P1 will be the one that picked first and P2 will be the second)
Then P2 strikes a stage from the random select followed by P1 doing the same. They then play on the randomly selected map.
That map and any other map can't be played on for the rest of the set. The stages stricken from the random are then open to play for the next game.
The loser of that game then chooses what stage they will be playing on for the next round. The winner then chooses their character. Lastly, the loser can choose a different character. Then they play the next round.
Repeat until the set is over.
If you want to know how to counterpick, then it requires you to know character match-ups. If you know you do bad against Marth, then, if you lose to one, you need to pick a level that gives you an advantage over him and/or play a character that does better against him.