There really aren't too many advanced techs with Luigi, he's a pretty straightforward character compared to most, but he does have some pretty cool stuff he can do his jab can combo into a lot of things such dsmash, up-b, and grab. Mashing down-b will give you a boost to help you recover. Dthrow and uthrow can both be used to combo into usmash at low percents, or to set up for air combos, you'll want to use uthrow for fast fallers and dthrow for pretty much everyone else, dair has a tiny meteor smash hitbox that is really hard to hit, and down taunt deals 2% damage and sends your opponent straight up, but not high enough to kill them, however if done while they are on the ledge it will send them straight down, this is a guaranteed kill regardless of percent and is the ultimate humiliation tactic.
Edit: Those are just a few things, but also go check out Luigisama and Yoshq's advanced tech video.