This match-up is scary against a good Luigi player, but as long as you play safely you shouldn't have too much trouble. You're going to need to be very precise so that you don't get punished, though.
As everyone has said, you need to camp Luigi. Don't bother ever approaching unless you're not in the lead anymore. He's basically Dedede with more dangerous kill moves and a far less annoying grab since he's so slow and gets camped hard (he has his Cyclone, though, so that helps him quite a bit since it's so fast). You'll want to bait Luigi into unfavorable positions (like him being above you) to make it easy to punish his movements. Luigi will try the same to you by attempting to apply constant pressure, but as was said before if you find yourself in a bad position try double-jumping away to reposition yourself. Luigi really can't do much about characters whose
air-speed match his own ground-speed.
So yeah, it's a problematic match-up when one of the least mobile characters is paired up against one of the most mobile. Mobility is the key to succeeding in this match-up. As long as you don't try to do anything stupid like dash-grabbing into Luigi from a neutral position (have fun getting up-B'ed), he really can't do much to you. I think Luigi's most reliable kill move in this match-up is his n-air, which can kill Yoshi around 145% if he keeps it fresh, I think.
Oh, one more thing. While recovering, Luigi's side-B can get beaten out by Yoshi's f-air. It takes really precise timing, though. Otherwise the f-air doesn't come out in time or they trade, and trading with Luigi is usually a bad thing, so only do it if you are sure you're going to net the kill.