Back out the screws that secure the old sill in place with a drill and Phillips drill bit. Cut through the sill's caulked edges with a utility knife. Insert a pry bar underneath the old sill. Push down on the pry bar's handle to lift the sill up and out of the door opening.
Rip a 1/4-inch hardboard to the same width as the replacement sill, using a circular saw. Insert the hardboard in the door opening, between the side jambs.
Spread a scribing tool to the widest gap between the jamb and the hardboard. Trace the scribing tool down the jamb to transfer the jamb's contour onto the hardboard. Remove the hardboard from the door opening and use a jigsaw to cut the board along the tracing. Use a saw rasp to fine-tune the tracing's corners.
Measure the door opening and transfer this measurement to the new sill. Cut the new sill to this length. Use a circular saw for wooden sills or a jigsaw for metal sills. Hold the template over the new sill and transfer the jamb's contours onto it.
Cut the new sill to match the contours. Use a jigsaw to make these cuts in both wood and metal sills. Smooth the cut edges and clean up the contour's corners in the new sill with a rasp saw or metal file. Drill 1/8-inch pilot holes through wooden sills. Place one screw on either end of the sill and on in the center. Keep the end screws about 2 inches in from the ends. Metal sills have pre-drilled screw holes.
Place the new sill into the door opening. Secure the sill in place with screws. Insert a tube of silicone caulk into a caulk gun. Cut off the caulk's tip with a utility knife. Run a caulk bead down the sill's edges. Run a fingertip down the bead to smooth it.