Insert the tube of exterior-grade caulk into the caulking gun with the tube nozzle pointing away from the trigger. Apply a thick bead of the caulk at the edge of the flooring, as well as a generous amount of caulk over the area where the door saddle will sit, with the bead of caulk at the edge of the door nearest the exterior running the entire length of the door opening.
Slide the wood door saddle under the doorstops -- the narrow strips of wood running around the center of the door frame -- and up against the edge of the flooring. Push down on the wood, seating the saddle into the caulk.
Use a 1/8-inch bit to drill holes at each end of the threshold and two more holes equally spaced across the doorway. Screw a 1 1/2-inch, galvanized wood screw into each hole. Countersink the head of each screw. Fill in above each screw heads with wood putty. Use your finger or a putty knive to wipe the putty flush with the surface of the wood.
Caulk around the edges of the doorstops on each side, where they meet the wood door saddle.
Fit the door saddle in place over the joint where two flooring types meet in a door opening. An interior door saddle has several forms; be sure to purchase the correct one for your situation. Different door saddles are designed to bridge the transition from carpet to smooth flooring, between two different types of smooth flooring, and between two different floating laminate or hardwood floors.
Drill pilot holes -- with a bit slightly smaller than the diameter of your screws -- at each end of the threshold trim where they will hit the subfloor beneath, rather than the flooring on either side. Screw in a wood screw of the appropriate length to secure the saddle to the subfloor. Countersink the head of each screw.
Fill the holes above each screw head with wood putty. Use your finger or a putty knife to wipe the putty off level with the surface of the wood.