Set up a suitable place to paint, such as a garage or unused room with plenty of ventilation and space to move around. Prepare the area by placing newspaper under the chair. Wear a face mask.
Turn the chair upside down. Apply the first coat of paint to the upward facing surfaces---what would normally be the underside---with a brush. Allow to dry. Turn the chair upright. Paint the rest of the chair, beginning at the top and working downward. Reach all the nooks and crannies. Brush out runs in the paint immediately.
Lightly rub the chair all over with fine grade sandpaper to ensure a smooth finish. Wipe the chair with a damp cloth soaked in water for latex or white spirit for oil-based paint.
Paint on the second coat as described in Step 3. Usually two coats will be sufficient for a plain finish.
Seal and protect latex. Apply two coats of polyurethane varnish with a paintbrush. Sand the chair between applications and wipe with a cloth dampened with white spirit. If you used oil-based paint, you don't need to varnish. Allow the chair to stand for at least 72 hours before using it. This gives the finish time to harden and "cure". Keep children and pets away during this time.