Cut the first piece of baseboard to the proper length at 90 degrees and nail it to the wall with the flat end against the wall perpendicular to the wall to which it is attached. Mark the remaining piece of base board to its proper length along the top edge.
Set your miter saw to a 45-degree miter. Position the baseboard on the saw with its back against the fence and its top up. Set the miter to cut toward the mark, so that the mark is on the short edge of the miter. Set the saw for a left miter to cut the right end of a left hand piece, and vice versa.
Start the saw and cut down through the baseboard in a single smooth action. Release the trigger and allow the blade to stop spinning before letting the blade return to its upright position. Use a pencil to mark along the profile edge on the baseboard, where the miter breaks.
Clamp the baseboard to your work table with this end extending into space. Use a coping saw to cut along the profile line you marked in the previous step. Keep the saw perpendicular to the molding. Cut along the line until you completely cut from top to bottom.
Fit this "coped" edge against the baseboard you nailed to the wall. Fit the coped molding flat against the wall with its coped end snug against the other piece. Nail it to the wall as you did the first piece.