Neutral A: Tapped once, Mario just weakly punches the opponent. Hit 3 times, he will punch high, then low, then kick.
DA: Mario slides, baseball-style, into the other opponent. This is one of the better running attacks in the game, as it is quick, provides good power, and sets up for a throw.
Utilt: Mario performs an uppercut, knocking the opponent a little ways into the air. Great for starting combos, but long cool-down time, so be careful.
Dtilt: Mario crouches and kicks one leg out. Short range, low damage, and long cool-down time make this attack practically useless in high-level combat.
Ftilt: This move is Mario's roundhouse kick. This is useful for getting some breathing room, as it sends your opponent a fair distance (for a tilt), and the cooldown time is lower than any of Mario's other tilts.
Usmash: This one is Mario's killing move, especially against lighter characters like Kirby and Pikachu. He head butts the space above him, and with a head that can break bricks, you know that's going to hurt. Sends the opponent straight up, and hopefully out.
Dsmash: Who knew Mario could breakdance? Mario gets on his hands and spins his legs around his body at floor level, first to the front, then to the back. A very powerful edgeguard, and great for clearing out a rolling opponent.
Fsmash: Mario unleashes a massive punch, his fist getting rather large as he does so. This attack can be tilted up or down by pointing the control stick after starting the smash. Also a good edge-guarding move, though generally too slow to use in even combat.
Uair:
B-attacks:
Neutral B: Mario throws one of his famous fireballs. No one can say exactly where they come from, but he seems to have an infinite supply. These are Mario’s crutch when up against a faster opponent. By slowing your opponent down, you have time for Mario to get close and do some heavy damage. Because these fireballs drop and bounce, they are also great for edgeguarding and preventing edgeguards.
Up-B: Another famous Mario move, he jumps into the air, knocking coins out of anyone he hits. If he catches someone with the beginning or middle of this attack, he can carry them with him, knocking out one coin and 1% dmg for every hit. This attack takes Mario up at a slight angle, so make sure that you aim yourself properly so that you don't bounce off of the bottom of the level.
Down-B: Not sure exactly which Mario game this was from, but this is the Mario Tornado. Our Italian protagonist spins around in place, hitting anybody nearby while pulling them into him, and then he stops and throws his fists out to either side, sending opponents flying.