Take down the measurements for the walls. Measure each wall with a measuring tape, and write down the numbers on a piece of paper.
Transfer the measurements from the paper to the baseboard molding, using a pencil.
Cut the baseboard molding to size, using a handsaw and miter box. Place the baseboard molding in the miter box. Cut the molding at the appropriate angle with the handsaw. Both inside and outside corners can be cut by locating the 45-degree angle in the box and placing the handsaw at that angle while cutting the molding.
Set the baseboard molding against the wall and the floor. Have an assistant hold the molding in place while you hammer it in with finish nails. Space the nails 6 inches apart. Sink the nails below the surface of the molding with a nail set.
Fill the nail holes in the baseboards with wood putty. Let the putty dry, and lightly sand it until it is smooth.
Caulk the gap between the baseboard and the wall. Let the caulk dry, and then paint the baseboards as desired.