Prop the door open and see how the sill plate is secured. Wood thresholds may be fastened with either nails or screws, and metal ones are usually secured with screws. Remove the fasteners. Unscrew the screws with a screw gun or a hand screwdriver. Slip a pry bar under nailed wooden sill plates and lift it gradually until the nail heads pop up and can be removed with a nail puller.
Clean the area under the old sill with a vacuum cleaner and make sure there is no rot or other damage to the floor underneath. Scrape away any caulk or adhesive with a scraper. Fill nail or screw holes with epoxy automotive body filler or wood plugs pressed into the holes.
Use the old sill plate to mark the length on the replacement. Cut the new one to size with a hand saw or power saw. Test it for fit underneath the door stops, the vertical strips on each side of the door; trim the door stop if necessary with a small hand saw, such as a drywall saw. Slide the new sill in place and make sure it fits properly, check it with a level and make sure the door will close easily and firmly.
Remove the new sill and put a bead of caulk under it in the center; run the bead down the center of the sill plate area on the floor as an alternative. Slide the new plate in place and secure it with screws, which should come with it. Use finishing nails on a wooden sill if desired; countersink the heads. Verify that the door closes correctly.