Unscrew all hardware from the furniture, including knobs and hinges. Lay tarps or newspapers around the floor surrounding the furniture. If the furniture is attached to a wall, lay painter’s tape around the perimeter of it to protect the wall.
Brush chemical stripper in one direction onto the surface of the furniture. Start from the top and work your way down. Cover the wood 1 or 2 square feet at a time, letting the stripper soften and ripple the paint or gloss finish on the furniture.
Scrape off the softened paint or old varnish with a plastic putty knife, scraping with the direction of the wood grain. Repeat over the entire piece of furniture, adding more stripper as needed, until all the paint or gloss is off the surface.
Put on gloves. Dip a nylon wool scrubber in paint thinner. Scrub the piece of furniture with it from top to bottom, taking off any residual finish and getting the surface smooth and clean. Let it dry for 12 hours.
Sand the whole surface with fine sandpaper by hand, smoothing out the wood. Wipe off the dust.
Brush varnish in one direction onto the wood surface with a paintbrush, starting at the top and working your way down. Brush it on in a thin, even coat. Let it set overnight.
Sand the varnish by hand very lightly so it just dulls the shiny surface. Add a second layer of varnish in the same manner as the first. Repeat the process for a third layer. Let it set for 24 hours.