He's the man in green lol. gona post later.
Edit: Hmm. There's so much about to Luigi, I don't know where to start. Basically Loucan's guide sums everything up but I'll give out important pointers.
I think of Luigi as a aerial offensive but in reality, he's a balanced character because he fights differently accordily to whom hes fighting (close, sword, projectile user).
Luigi isn't one of those character's that you just pick up and already mastered him. Like every other character, he has to be well praticed, dedicated. He could take days or even months if you want to reach his full potential. A character like him a full potential is very deadly.
Luigi's power lies in his aerial game. He can fit 2 aerials in one short hop. He can string and/or connect his attacks easily. He can rack up damage at lower %s as quick as sonic's speed. His utilt lets him give you a quick 30% right off the bat, even more against fastfallers/heavy weights. He has ok ground game, but it mostly lies in aerial game.
He has alot of kill moves and some of them can kill at pretty low %s His Fsmash and shoryuken can fairly low %s. His Nair, Bair, dsmash,upsmash, arre his other main kill moves.
What Luigi lacks is really, his range, low priority on some moves, very floaty, he lacks the air mobility.