Remove hardware such as drawer knobs or hinges, if any, from the project piece. You might need a Phillips or flat head screwdriver. If you wish to leave the hardware intact, cover it completely with painter's tape to avoid marring or painting it.
Cover the project area with newspaper or a tarp. Set the project furniture atop the paper.
Sand all of the paintable surfaces using a fine grit sanding block. Sand just enough to scuff the top layer of the project a bit to create a better grip for primer. Wipe the dust away with a tack cloth.
Pour some of the primer into a paint tray. If the furniture has drawers, remove them so you can prime the front of the piece properly, then stand them up with their fronts facing up. Dip a paintbrush into the primer and coat the entire furniture piece. Prime the faces of any drawers. Allow the primer to dry completely. Apply a second coat if the stain is still visible beneath the primer, and allow it to dry.
Stir the paint with a stir stick and pour some of it into a paint tray. Apply paint to the project with a paintbrush, using smooth, even strokes. Allow the paint to dry per the manufacturer's instructions. Sand the surface gently with a fine-grit sanding block, wiping away dust with a tack cloth. Apply a second coat and allow it to dry.
Apply a coat of glossy polyurethane sealer over the finished piece for added protection using a paint brush. Brush out drips on the furniture piece as they occur, using care to paint the sealer on with even strokes. Allow the sealer to dry completely. Apply a second coat, if desired, especially if the piece is handled or used frequently. Sand gently with a fine-grit sanding block before applying the (optional) second coat, wiping away dust with a tack cloth.