The classic method of approach with Luigi is the fire ball, then running grab read. Your opponent is predicted to shield, giving you the chance to dash grab them. It uses one of Luigi ' s weaknesses and turns it into his strengths.
Another is a side b fake out, followed by a down tilt then immediate grab out of shield. This is for mind games primarily, and won't catch them off guard if they spot it.
The next is actually after aqquiring the down throw. Instead of following up with the usual combos, go down with a down b cyclone. Mash the b button for max effect. It will trick your opponent into shielding so you can go for another grab, dealing an extra 10%, followed by a combo of your choice.
Upthrow to up air is another low percent mix up that will condition them into air dodging.
Simply hovering with a single short hop every few seconds, followed by a forward tilt is an excellent mind game and can be used to get the drop on the opponent if it hits. But be careful, it's easily punishable.
In conclusion, Luigi is all about patience and waiting to turn defensive positioning into a mounting offensive. The biggest issue with anyone who mains Luigi is frustration after not getting an activity. You have to adapt, be fluid, like rain. Then transform to lightning in a single movement.