First I want to be clear, this is not an accepted method. And the only reason I suggested was that I think the door is a write off and doing anything to get a few more years would not hurt.
I spent an hour searching the net for teaching aids and found nothing.
First I wold like to point out things about your door. The quallity of the wood that is not rotten will have a lot to do with how a repair will work.
If you do a google search on (repairing exterior door frame) you will find many repairs being done but what you rarely find is the door in worse shape than the frame. That is because the door is usually made out of better wood than the frame is.
Now go up and look at the pictures you posted the frame looks in good condition and is why I pointed out poor wood being used and they knew it when they built it. The styles of the door or the long peices of wood running up both sides and are usually machined to take the panels in this case you can see they added better wood for the machining for the panels.
Now how I would repair the door
1. find the replacement wood and have it matched to the thickness of the door and wide enough to replace the area and the sides have to be absolutely square to the surface. a little to long is good.
2. do a hunt and find screws long enough to reach thru the repacement wood plus 1 1/2" . Something like 8 or 10 inches, they are out there.
3. Predrill the repair wood from the bottom up with a hole just big enough for the screw to slide in with out a fight but not to loose. Then countersink those holes so the heads of the screws will not be prodruding when installed.
4. You need a circular say that will cut an absolutely square cut and must be checked, a 24 tooth blade that come with a new saw should be fine but some test cut would be helpfull'
5. You will need a peice of 1/4" plywood say 40" x 8" that you can clamp or tack to the door so the saw can follow it for a straight cut.
6. measure how much you want to cut off and draw a line there. then measure the table of the saw most measure around 5" from the fat edge of the table to the near side of the blade.
7. Tack or clamp the plywood that far away from that line of the cut
8. the deepth of the saw can be adjusted you want to make sure the motor of the saw isn't so low that it will hit the plywood, that would screw up the cut.
9. Apply exterior wood glue and screw the peice into place, wipe off eccess glue right away
10. Your peice iis a little to long and will need to be trimmed, but most doors have edges that are not quite square, like five degrees, the saw will have to be set to match that.
11. Do not replace the metal thing on the bottom of the door as that likely really helped the problem get started.
Aren't you glad you asked?