Measure the gap at the base of the door, noting height, width and depth. Use a drill to remove the door from the hinges and set it on the working station.
Cut a two-by-four to fit the gap under the door but still leave a 1/4-inch space. Hold the board against the base of the door and drill four holes through the board and into the door. Apply a bead of caulking to the board and door. Attach the board to the door with 5-inch wood screws. Attach weatherstripping to the bottom of the door board.
Set weatherstripping in place on the threshold of the door. Cut off any sections that need to be removed or adjusted for a perfect fit using a scissors or utility knife.
Remount the door by screwing it back onto its hinges with the drill. Shut the door and determine if any adjustments need to be made with the way the sill extension and the threshold touch each other. Make any necessary adjustments.