Fake wood grain paneling is composed of high-density polyurethane manufactured to provide an cheap alternative to actual wood panels. Unfortunately, unlike actual wood, these panels are slick and nonporous making them poor surfaces for paint adhesion. If you would like to paint over fake wood grain paneling, you will need to apply a bonding primer, first, or the paint will peel up. In addition, you will need to abrade the surface to promote adhesion before you prime, or the primer will chip away over time.
Clean the fake wood grain paneling using soap and wet rags. Rinse away all soapy residue. Allow the surface to dry completely.
Cover flooring adjacent to the fake wood paneling with fabric drop cloths. Cover any areas you do not want painted with tape.
Abrade the paneling to promote adhesion by sanding it with a palm sander loaded with 300-grit sandpaper.
Apply a thin coat of primer to the paneling using the roller. Allow the primer to dry for three hours. Apply primer to any areas of the fake wood grain paneling inaccessible to the roller using the paintbrush.
Apply two thin coats of interior acrylic latex paint to the paneling in the same way you did the primer. Allow two hours of dry time between coats.