The first step is to remove any hardware that is existing on the cabinetry.
Then, use a sanding sponge to rough up the surface of piece with sandpaper or a sanding sponge. once you've scuffed it up, wipe the entire piece down with a damp cloth and let it dry.
To ensure a nice and lasting finish, prime the piece with a bonding primer and let it dry.
Next, the paint. For a bathroom, I recommend an enamel paint, it has a tougher finish and will hold up nicely to the wear and tear a bathroom sees.
Finish the cabinet with at least two coats of paint for both coverage and durability.
Add some fresh hardware that really speaks to your taste and you've got a whole new vanity for very little money. I'm Mrs. Fixit and it's just that simple!