Remove the old threshold, typically screwed into place, with a power drill and screw tip. Inspect the anchoring points in the concrete; if they are in good condition, use them again. Replace any defective anchors and patch any damaged concrete with a good concrete patching material. Drill holes with a concrete bit if necessary to install new screw anchors.
Measure the width of the door frame and the height of the threshold above the bottom of the doorway with a tape measure. Buy a replacement metal threshold the width of the door; you may have to cut a metal threshold with a hacksaw to make it fit. Make sure it is wide enough to extend outside the closed door on both edges. Get one with a rubber insert in the top to make a firmer but flexible seal.
Set the new threshold in place and test the door to make sure it closes easily and securely. Run a bead of caulk under both edges of the metal threshold. Fasten the threshold with screws. Use galvanized metal screws through the holes in the threshold into anchors in the concrete or use special concrete screws to go into a concrete base. Make sure all screws are flush with the top of the threshold and will not interfere with the door.
Follow similar steps if there is a wood base at the bottom of the door frame. Fasten the replacement threshold with wood screws in that case.