Wipe down the furniture with a damp cloth to remove any dust. If your piece has drawers or doors, remove them and work on the pieces separately, but at the same time as you work on the body of the furniture. If your furniture has touch stains or residue, use a household cleaner to remove them. Let the furniture dry. Lay down a drop cloth beneath the furniture before you begin painting.
Apply a coat of oil-based primer to your furniture. Alternatively, use fully cured shellac primer to cover the laminate. Primer is always an important step, but especially so when covering cherry laminate, because it is dark. Water-based primers also work, but will require you to fully sand the furniture and wait seven days before you paint. Oil- and shellac-based primers dry in just a few hours and stick to the laminate without the need for sanding. Use a roller to apply the primer to large surfaces, and follow up with a brush to get into decorative cutouts or corners.
Wait for the primer to dry for the amount of time recommended by the manufacturer. Lightly sand the furniture with a medium-grit sandpaper, such as 120-grit, to clean up any primer drips or noticeable paint stroke marks. Use a damp cloth to clean up the dust created by the sandpaper.
Apply your top coat of paint over the primer. Latex-based paint will work, even though the primer was oil-based. Use long, even strokes with the roller to apply paint to larger surfaces. Apply paint to the decorative cutouts and corners using a high-quality brush, to minimize stroke marks. Let the first coat of paint dry per the manufacturer's instructions before adding a second coat, if necessary.
Allow the paint to dry overnight before you reassemble any doors and drawers. Wait a few days before you return the furniture to regular use, to allow the paint to fully cure.