If the door is in rough shape it will need to be refinished.
OLD DOORS HAVE A HIGH LIKELIHOOD OF CONTAINING LEAD PAINT. PLEASE USE THE NECESSARY PRECAUTIONS WHEN CUTTING AND SANDING LEAD PAINT.
Check if your door is solid wood or a veneer (a thin layer of pretty wood glued over strong but not-so-pretty wood). Check the edges. If you have a veneer, make sure it is thick enough to sand off the finish. Do some test sanding on your cut-off piece.
Sand off the old varnish and stain. Start with 100-grit sandpaper, then 180, then 220. You may need to make some sanding jigs to sand around your molding.
Sand down a piece of the part you cut off earlier for testing stains. I used a 1/4-sheet palm sander for most of my work and a wood block and sanding jigs for the smaller areas.