Answer:
You cannot play as mew in Melee, however, you can summon him out of a pokeball, I can't remember exactly what you have to do to make him able to appear out of pokeballs, but I'm sure you'd be able to find out on a gaming website. But, to answer your question, you cannot play as him.
To get mew from a pokeball, you must unlock all characters and get lucky with a pokeball.