Prepare your properly ventilated work space outside or in the garage by laying out large amounts of cardboard on the ground. Place the wooden toy box on top of the cardboard and arrange your materials nearby. Put on your gloves and safety goggles.
Apply paint stripper to the toy chest using a "natural-bristle" paintbrush if the object is painted. If your toy box is stained, not painted, apply varnish remover. Allow the paint or varnish remover to sit on the toy box for the recommended amount of time.
Scrape off the old varnish or paint using a paint scraper or wire-bristle brush. Be careful not to scratch the wood. Continue to apply stripper or lacquer-thinner and scrub with a wire brush and cloth as needed to remove any residual stain or paint that you were unable to remove on your first attempt.
Allow the stripped toy box to dry overnight.
Apply your choice of stain to the toy box and let dry.