Remove everything from the furniture surface, drawers and shelves.
Wipe down the surface with a dust rag. Use the screwdriver to remove screws from the furniture to take the pieces apart. Remove handles and knobs as well.
Lay each piece on a large drop cloth or old towels. Apply a coat of white primer paint with a foam brush to all sides of each piece. Wait for the coat to dry, and then apply one to two more coats. Wait for each coat to dry before adding another coat.
Paint a coat of acrylic paint of the color of your choosing on all of the pieces. Wait for the paint to dry. Apply additional coats until the white primer does not show through.
Allow the final coat of paint to dry. Apply clear acrylic varnish to all surfaces. Allow the varnish to dry, and then apply a second coat if desired. Let the coat dry fully.
Put the pressboard pieces back together. Be careful when reinstalling the screws -- too much screwing pressure could cause the pressboard to crack.
Replace all removed knobs and handles.