To play as Luigi, pass the Bonus Practice 1 with at least 8 main characters. When Luigi challenges you, defeat him and he's yours.
Complete the game on Normal with any character without using a continue, then battle Ness and win.
To access the hidden classic Mario stage (complete with POW signs, Piranha plants, warp tubes and elevator), beat the game's one-player mode with each character. At the end, the game will tell you that you can now access Classic Mushroom Kingdom in the versus mode.
You can change your character's outfits by tapping the four C Buttons at the character select screen. Some costume changes are limited to colors, but characters like Pikachu are also available with a hat.
To play as Captain Falcon, simply beat the game as one of the regular characters. When Captain challenges you, defeat him and he will be a playable character.
To play as Purin, play a game as Captain Falcon. After you beat the game Purin will challenge you. Defeat her and you will receive the second Hidden Character.
Beat Bonus Stages one and two with all 12 characters. You need to have unlocked the four secret characters first. Now go into the Data section.