Training mode can help you learn some of his combos.
Dthrow/uthrow chaingrabs on like, everyone. I've noticed that Mario can dthrow chaingrab Lucas to like 50%.
Dtilt is really useful for combos, and you can cancel the first or second hit of jab into all tilts or dsmash.
Fireball hit confirms into almost anything, but useful ones would be dsmash and fsmash for finishers.
Dthrow/dtilt to fair or nair
You can dtilt to utilt at low percents (like 40%, since at 40% dtilt will knock almost any character upwards and into hitstun for free followups) and follow up with something like uair or nair.
I haven't found many uses for ftilt, except for some times where I can use it to finish a combo off if the opponent is within reach. Sometimes if they are at too high a percent to dtilt into nair or something, I'll do fireball confirm to ftilt. It's useful to setup edgeguards since it comes out really fast.
And any other combos Nameless mentioned :D otherwise, just practice your combos and followups in training, that what I did.
I have a question also: what are some good uses of jab reset for Mario?