For every Luigi mission you first need to visit him at the Sex Club 7.
You need to go and pick up Misty, who is Luigi's girlfriend, so follow the radar to her location. Once you've got her in the car, simply drive back to Luigi to drop her off.
Reward: $1,500
This mission involves sending a message to a drug dealer. Take the bat from across the road and acquire a vehicle to head towards the objective. Once at Portland Harbor, you'll need to beat the drug dealer with your bat until he's bleeding. You then need to steal his car and get it sprayed, before storing it in the garage marked on your map.
Reward: $1,000
This mission introduces you to guns in GTA III. Head to AmmuNation and try out the target range. You then need to go to the car marked on the map and ram it until the driver gets out. Once that happens, run him over to complete this mission.
Reward: $4,000
The Fuzz Ball is a timed mission. You have 5 minutes to pick up Luigi's girls and drive them safely to a ball. Make sure you get a car that can fit them all!
Reward: $2,000 - $4,000