Strip the original finish. Depending on how the furniture was sealed, you have different options for products to use. Denatured alcohol is best for shellac and lacquer finishes. Mineral spirits, paint thinner and varnish thinner will work for most other finishes.
Dab the appropriate solvent onto the wood with a rag soaked in the solvent. Allow the solvent to sit for about 10 minutes or as the manufacturer directs. These products do vary so read all labels before using them.
Peel the old finish from the furniture with a nonmetallic paint scraper and scrub brush. As you work, you may notice that some of the finish won't come up. If this happens, apply more solvent and keep scrubbing until the wood is bare.
Wipe down the wood with a damp cloth. This will remove any bits of finish, streaks and residual solvent. Allow the wood to dry completely.
Mix the primer as the manufacturer directs. Pour the primer into a small bucket or paint tray. Spread the primer over the wood with a roller or paintbrush; natural or synthetic bristles are fine. Use full, even strokes and always go in the same direction. Allow the primer to dry.
Mix and apply a coat of paint using the same process as you used with the primer. When selecting paint, make sure it is compatible with the primer. For example, if the primer is water-based, the paint should also be water-based. Allow the paint to dry and apply additional coats, if desired.
Seal the wood with a wood sealer that is compatible with paint. Polyurethane is a common option because it is durable and comes in matte, satin and glossy finishes. Pour a small amount of the desired polyurethane onto the wood and spread with a foam or lamb's wool applicator.
Spread the polyurethane as thinly as possible. This will help it dry and provide a full, even coat. Overlap each pass with the applicator by at least 1/2 inch. Allow the polyurethane to cure overnight.
Scuff up the surface of the polyurethane with a piece of 400-grit sandpaper. Wipe the furniture with a damp cloth. Apply up to five coats of polyurethane in this fashion. Two is typically enough for the average project but you should use more if the furniture is used heavily.