Remove the old threshold by unscrewing any screws that hold it to the floor. Set the edge of a pry bar between the threshold and the floor, and apply pressure carefully. Measure the width and length of the old threshold once it is pried loose.
Purchase an oak threshold strip at a home improvement store. Choose one that is no more than 3/4 inch high and matches the width of the old threshold. Cut the new threshold to match the old length exactly, using a power saw for clean edges.
Set the new threshold in place for a dry fit. Trim the ends as necessary until there is an exact fit and the ends press against the door frame with no gaps. Use the old threshold as a template to shape the edges for a proper fit.
Sand and stain or paint the new threshold to match the decor. Allow it to dry for 6 to 8 hours. In the meantime, clean out the threshold area of any debris, dried adhesive or mold.
Spread construction adhesive all along the bottom of the new threshold piece and press it into place. For exterior door thresholds, ensure that the downward slope of the piece faces away from the house to help keep out water. Countersink flat-head screws into the threshold in the center and on each end.
Insert 1-inch pieces of dowel into each of the countersunk screw holes to ensure they will work as wood plugs. Remove and coat the end of the dowels with glue. Reinsert them into the screw holes and let them dry from 4 to 6 hours.
Trim the dowels so they are even with the surface of the threshold, using a trim saw. Stain or paint the wood plugs to match the threshold.
Apply caulking to the seam where the doorjambs and threshold meet to prevent water from seeping in. Allow it to dry completely, about 6 hours. Apply a clear polyurethane finish to protect the wood threshold. Let it dry for 24 hours.