Tear it down before rebuilding! Before installing an exterior door, go the distance to discover and demolish all the rotted wood damage caused by leaking gutters and the backflow of rain toward your home's foundation. Digging deeply to expose all the wood rot also exposes the solid wood you will use as the foundation for hanging the replacement exterior door.
Tear out all the rotted wooden components of the doorway until solid foundation lumber is exposed for the replacement exterior door. Remove the door, threshold, door frame, exterior siding, frieze board, and rotted ends of the wall studs, as necessary.
Cut two-by-fours to replace portions of rotted wall studs and framing removed around the exterior door. Drill pilot holes and secure replacements to the remaining studs/framing, to each other, and to the floor decking with 3-inch rust-proof screws.
Reinstall the old insulation or replace it with new batting to insulate around the new framing for the exterior door. Be sure to handle fiberglass batting with gloves and use safety gear to protect yourself from the fiberglass particles.
Cover the repair area around the exterior door with siding, lifting it off the ground while sliding the edge under the existing siding sheet. Secure it with hot-dipped galvanized nails to secure it to the framing.
Re-cut the exterior door opening. It could have been cut before the siding was mounted, but a router bit that follows the interior door frame as a template makes a perfectly sized opening with a clean edge.
Rest the exterior door assembly on the threshold, making it plumb and level with shims, if necessary. Secure the hinged side with long screws driven through the hinges, frame, and shims, and then into the house framing.
Secure the unhinged side of the exterior door assembly, driving finishing nails through the door assembly and two-by-four house framing. Be sure to catch any shims with the nails to prevent them from shifting.
Position and re-nail the original frieze board removed earlier as part of the exterior door demolition. It will be the last component to reinstall, resting on top of the siding. Add the knob and latch hardware associated with the new door.
Fix the source of the exterior door's wood rot. Add/fix gutters to catch water running off the roof. Add plastic sheeting beneath rocks and other landscaping materials immediately adjacent to the house to make water run away from its foundation.