Sand the surface of the wood by hand using coarse, then medium, then fine-grit sandpaper or using an electric hand sander. This will remove any protective varnish, which could repel paint, and will also leave you with a smooth surface on which to apply the new coat of paint. If you use a primer designed to be applied over wood stain, you can skip this step.
Apply a coat of stain-blocking primer to the prepared surface using a soft brush for furniture or small areas and a roller for large areas such as wood-paneled walls; use long, even strokes to ensure smooth coverage. If the wood you are painting over is stained a light color, you may be able to use a regular oil-based or latex primer. If the wood stain is very dark, a tinted primer is best.
Allow the primer to dry completely. This could take between two and 24 hours, depending on the thickness and type of primer. Latex primer is generally dry to the touch in under 2 hours but oil-based primers need a full 24 hours of dry time before applying another coat.
Apply a layer of latex paint or enamel over the primer using the same method as before. Work in large sections using long, even strokes to be sure that you do not miss a spot as you are painting. You should be able to see a difference between the dry primer and the wet paint, which will make it easier to notice the places where the paint may be too thin.
Let the first coat of paint dry completely. Latex paints and enamel may be dry to the touch after a few hours but it is wise to leave 12 to 24 hours between coats to ensure that the paint is completely dry.
Apply a second coat of paint if necessary. If the first coat is opaque enough to cover the wood stain and you did not miss any spots, one coat may be enough. Adding an extra coat, however, may make the paint job last longer and it may stand up better to cleaning.