Ok then, but bere in mind that I'm going by instinct here, not being able to see the job, and I'm only telling you the easiest . not necessarliy the best method at the moment.
Since the door is already too short, that is actually a goodish sort of thing, because it will fit in the doorway in at least one direction.
Remove old door. Sit new door in doorway (at this a stage get a wife or neighbour to help you for a mo). Whilst you hold the door in as square a position as you can, get your assistant to draw around the door frame onto the door. Ie so that you have the outline of the door frame on the door. using a circular saw if poss, (if not - a handsaw and planer) cut the door to fit, taking off about an extra couple of mm. I should point out that if at all possible, try to take off about the same amount each side, rather than just all off one side - it will make it stronger and look better. (you'll obviously have to adjust your marks by approixamtly half each side).
Once the door fits fairly snugly, fix your new strip on to the bottom (NOT THE TOP) of the door and just check the fit again.
Fit hinges, and plane down so the door fits, idealy with about 2mm (the width of a twopenny coin) gap all the way round.
Then fit your lock etc.
HOPEFULLY you will end up with a door that fits at least reasonably.
I really would be interested to hear how you get on - and thats not being nasty
Woody