Place the 1-by-8-by-12-inch board with the 8-by-12-inch side flat on a work surface. This is the seat.
Set the 1-by-8-by-4-inch boards on top of the seat at each end with the 1-by-8-inch surface perpendicular to the seat. These are the legs for the bathroom stool.
Center the 1-by-2-by-10 1/2-inch boards between the the legs on each side of the seat. The sides should be flush against the seat. These are the cross supports for the bathroom stool.
Hammer two evenly spaced finish nails through the legs into the ends of the cross supports at each joint. Turn the assembly over and hammer four finish nails through the seat into the ends of the legs.
Center the nail set over the nail heads and tap it with a hammer to set the nails 1/16-inch below the wood's surface. Fill the nail holes with wood putty using a putty knife. Allow the putty to dry overnight.
Sand the putty flush with the wood's surface with a fine-grit sanding block in the same direction as the wood grain. Wipe off the sanding dust with a tack cloth.
Paint the bathroom stool with a paintbrush. Allow the first coat to dry 4 hours and apply a second coat. Wait 24 hours before using the stool.