Scrape off any old, peeling paint using a sharp paint scraper. Be careful not to damage the wood as you are scraping. You only need to scrape the wood if the previous paint is peeling or chipping.
Wash the siding using a combination of 1 cup bleach and 1 cup trisodium phosphate per 1 gallon of water. Do not use a power washer, as it will damage the wood. Put the mixture into a garden sprayer that attaches to a hose and spray it onto the wall. If you have bleach, scrub it off with a stiff, nylon brush.
Rinse the siding with plain water, using the garden sprayer, and wait for it to dry.
Apply a water-based paint stripper to the siding, using a bristle paintbrush. This type of stripper breaks the bond between the paint the siding so the paint will peel off. Leave the stripper on according to the package instructions -- it can take up to 24 hours.
Scrape the paint off with a putty knife. The paint will peel off the boards.
Rinse the stripper residue off of the siding, using plain water in the garden sprayer. Wait for it to dry.
Paint on a high-quality, outdoor primer. Use a primer that complements the type of paint that was previously used on the siding, in case any residue remains. Never apply oil-based primer over old latex paint. It won't adhere. Use a bristle paintbrush to paint the primer on. Let it cure according to the package instructions and then apply a second coat. If you have had previous problems with mildew or live in a high-humidity area, you can buy primers that are designed to resist mildew.
Paint the siding as you did with the primer, using a bristle brush. Wait for the paint to cure and then apply a second coat.