Remove any existing finish by stripping it off with a chemical stripper, following the manufacturer's directions.
Sand the oak piece with medium-grade sandpaper. Sand again with fine-grade sandpaper. Finally, sand one more time with extra-fine-grade sandpaper. Wipe off any sanding dust with a tack cloth.
Mix one part water with two parts off-white flat latex paint. Stir to completely combine the water and paint. You should end up with a thin, opaque mixture with the consistency of heavy cream.
Brush the thinned paint mixture onto the oak furniture piece with a medium-sized paintbrush, using long strokes. Make sure you completely cover the piece with the whitewash. Work fast, so the paint does not have time to dry or set up.
Wipe off the excess paint after the piece is completely painted. Use a dry, soft rag and wipe it over the entire surface of your furniture piece, absorbing most of the paint.
Apply two coats of water-based polyurethane or water-based varnish, using a medium-size paintbrush.