Prop the door open with a brick or doorstop.
Put on knee pads and eye protection.
Make a cut from the front of the old sill toward the doorway, but stop at the frame.
Insert a pry bar under the cut in the old sill and pry upward and out. The rotting sill will likely break into two or more pieces. Remove the pieces with your hands and the pry bar.
Remove any nails that remain in the space using a nail puller. Vacuum out the empty space with a shop vac.
Measure the area where the old sill was installed with a tape measure. Measure and cut a replacement sill with a circular saw.
Fit the new sill into the space. If it has gaps underneath, lift the sill and place shims under it to make it flush with the entryway.
Push the sill back into place, then tap it into place with a hammer. Fasten the sill with stainless steel screws and a screw gun.