This story shows how to replace a door sill and threshold.
An exterior threshold takes a lot of abuse from foot traffic and weather, and it must be in good shape to keep the weather out. It can be replaced with a wood or metal threshold, either of which is available with a rubber gasket for sealing out the cold.
There is usually a sill below an exterior threshold. If the threshold is rotted, the sill probably is also. The sill is beveled on one side to drain water away from the house. Replace a sill using sill stock that has the same profile (shape) as the old sill. It fits tightly between wall studs and under the jambs and casing, so it has to be cut before it can be removed.
You may want to replace an interior threshold because the old one is ugly or because new flooring on one side of the doorway calls for it. An interior threshold simply rests on the floor with no sill under it.
2 or 3 hours
Circular saw or reciprocating saw, saber saw, hammer, chisel, nail set, tape measure, square, drill
Basic carpentry skills
Protect the floor with a drop cloth.
New threshold and/or sill stock, flooring adhesive, galvanized finishing nails, caulk