Clean out the rotten wood from the baseboard with a putty knife. Use the edge of the putty knife to remove as much of the loose rotted wood as possible.
Brush the rotted area back and forth in the same direction as the wood grain to remove any remaining loose debris from the baseboard, using a wire brush.
Apply wood hardener with a foam brush so it soaks into the rotted area of the baseboard. Allow the hardener to dry for at least two hours.
Fill the rotted area of the baseboard with wood filler. Pack it into the rotted area with the blade of a putty knife and even out the surface so it is smooth and slightly raised above the wood surface. Allow the filler to dry for 10 to 15 minutes.
Sand the filler with a progression of medium-to-fine-grit sanding pads so the repair is seamless with the surface of the wood. Always sand with the direction of the wood grain.
Brush on a coat of wood primer and paint using a paintbrush. Allow the primer to dry for at least four hours before applying a top coat of paint.