Many different airbrushes, I like Iwata brand.
SB Coat paint from Lure Works. This is a solvent based paint designed for soft plastic baits.
This is important, get a good paint respirator rated for organic vapors from solvents.
If you can't afford a paint booth rated for flammable materials, paint outdoors or in a well ventilated area.
This type of paint is very bad for your lungs and is flammable. Don't half ass the safety precautions.
Some people use water based paints and then dip in clear plastisol, I've never tried it.