You can prime and then paint. Or buy a paint that is primer and paint in one and do two thin coats (this kind of paint is for bathrooms I think but a girl at Home Depot recommended it). Do not paint the sides of the drawers or the inside of the chest because it's already a snug fit without layers of paint. I used a color called "West Coast Gray". Let it dry overnight.
Attach the knobs: Screw them in where you left a space between trims on each drawer.