Place some newspaper over your work surface or on the floor if you're working on the floor rather than a raised surface. Set the chair atop the paper.
Examine the chair closely, looking for any flaws such as splinters or rough wood. Gently sand any spots that need smoothing with a medium or fine grit sandpaper.
Wipe down the chair with a tack cloth to remove dust left behind from sanding.
Paint the chair with latex primer using a paintbrush. Allow the primer to dry completely.
Look over the chair to determine a suitable design and layout for your red and black color scheme. Write down the plan on paper if it's complicated.
Stir the red paint using a stir stick. Pour some of the paint into an old food container. Paint the entire chair red, unless certain areas, such as the legs, will be solid black, using a paintbrush. Leave the areas that will be solid black unpainted for now. Paint from the red paint you've poured into the old food tub rather than the paint container. Allow the paint to dry completely. Paint a second coat if the paint job seems too thin, allowing it to dry completely.
Cover areas previously painted using masking tape and newspaper if there's a risk of dripping black paint onto them.
Stir and pour some of the black paint into an old food tub. Paint any remaining areas that were earmarked to be all black. Allow paint to dry completely. Paint another coat of black if necessary, allowing it to dry completely.
Protect the chair with a coat of polyurethane sealer brushed on with a foam brush. Brush in one direction only, keeping the strokes steady and straight. Wipe up any drips as they occur, using the side of the foam brush. Allow sealer to dry completely before using the chair.