Open the exterior door. If possible, remove it from its hinges and set it aside. Insert a pry bar behind the toe kick (the vertical board underneath the door sill), and pull it away from the house. Set the toe kick aside.
Cut a strip of self-adhering flashing to the same width as the door opening. Peel off the flashing's paper backing, center the strip over the door sill, and smooth it in place. Remove all the wrinkles and air bubbles.
Measure the width of the door's jamb on the right side. Transfer this measurement to the new threshold, measuring from the threshold's back edge near the right side. Repeat this step with the door's left jamb. Connect the two marks on the threshold with a level and draw a line. Cut along the line with a jigsaw.
Cut a 12-inch-long piece of 1/2-inch plywood to the same width as the threshold. Hold one of the plywood's ends against one of the door's jambs. Open a scribe tool to the widest gap between the jamb and the plywood. Scribe along the plywood's edge to mark the jamb's contours.
Cut the scribe marks on the plywood with a jigsaw. Lay the plywood on the threshold and line up their edges. Trace around the plywood edge's contours to transfer them to the threshold. Flip the plywood over to create a mirror image on the threshold's other end.
Cut the threshold along the contour marks with a jigsaw. Slide the threshold into place from the outside. If it hits the floating floor, pull it out and sand the bottom inner edge with 120-grit sandpaper until the floating floor fits underneath it.
Slide the threshold back into place between the door jambs and over the floating floor. Set a level on the threshold. Slide wooden shims underneath the threshold to make it level. Score the wooden shims along the door sill with a utility knife, and bend them to break them off.
Spray expanding foam sealant underneath the threshold from outside. Set the toe kick in place, and nail it to the framing underneath the threshold that you pried it off in Step 1.
Put a tube of silicone sealant in a caulk gun and cut off the tip with a utility knife. Run a bead of sealant over the gap where the threshold meets each door jamb.