Instructions
The Hard Way
Find Vinnie's car, then locate the Pay'n'Spray on your map. Look at the route until you know it by heart.
Go pick up Vinnie's car. Wait for the alarm to stop sounding before you leave.
Move just a few feet so that the cops come and try to stop you.
HAUL IT! Drive to the Pay'n'Spray as fast as you can! Stay off the roads, the cops are deploying tire spikes all over the place! Driving this car without tires SUCKS!
Find a Wanted Level Reduction token if you can. There's one hidden in some trees a little ways north of Vinnie's car. This will take some of the heat off you.
Wait for the stars to disappear after you hit the Pay'n'Spray.
Drive to Vinnie's lockup.
The Easy Way
Enter the Never Wanted cheat (L1, L1, Triangle, R1, R1, X, Square, Circle).
Go pick up Vinnie's car and drive it to the lockup unmolested. Yes, the police come and say "Freeze!" but just drive past them. They won't shoot.