Put a tarp or plastic sheet under the chair to protect your flooring. Work in a well-ventilated area -- outside if possible.
Apply a chemical stripper to the wood. Buy a stripper that is specifically designed for pine; the label should say what kind of wood is appropriate. Paint the stripper onto the chair using a paintbrush. Allow it to sit for the time recommended by the manufacturer.
Use a scraper to scrape off the old finish. Do not scrape too deeply or you will gouge the wood underneath. Use a scraper with a rounded head so you don't scratch the wood with the sharp edges. Scrape off all the finish.
Sand the wood lightly. Start with 120-grit sandpaper, and work your way down to 220-grit. Wipe the wood with a tack cloth to remove the dust from the sanding.
Moisten an oil-based stain with a rag, and rub the stain into the wood. An oil-based stain works well for light wood like pine. Rub the stain with a lint-free cloth to remove any excess stain, and allow it to dry overnight. If you want the stain to be darker, repeat the staining process.