Sharpening a razor is a lot simpler than sharpening a knife, for the simple reason that the angle is provided by the combination of spine and edge. Get yourself a razor that is in fairly good condition, has been cleaned of rust and that has an edge that is fairly intact, by which I mean that the edge amounts to one straight line with no chunks of steel missing (oh, the specimens one finds at flea markets!). Then see to it that you have two or three sharpening stones from medium to fine or exta-fine. Then get yourself two level (flat) pieces of leather about 2x8 inches which you then coat with very-fine and very-very-fine polishing paste.
Then watch what Murray Carter has to say about sharpening a razor:
https://www.youtube.com/watch?v=vTV4ph1LE3c
If you want a really smooth shave, you usually have to go a step further than Carter recommends and use leather with polishing paste (he uses newspaper and things like that, nice to look at but not as effective as things can be, as he himself says). What I have discovered, after watching Carter videos, is that using a leather strop that is suspended in mid-air, like barbers use or used, tends to round out the edge and does not achieve the finest possible level of sharpness. A piece of leather lying flat on the edge of a table and coated with very fine polishing paste will give you the finest shaving edge ever (provided the razor has already been applied to medium to very fine stones).
One other very important thing: When sharpening the razor on the stones, the only real test for sharpness is optical. Keep working on the stone until the edge, while being pushed forward across the wet stone, begins to slide under the water on the stone. When the water and slurry and mud on the stone are being moved forward by the razor'#s edge, you know the bevel of the cutting edge is in full contact with the stone, and then and only then it is time to move to a finer stone or, if you already are on the finest stone, to the leather strop. The true test of sharpness when working with the strop is to apply the razor's edge to the softer hairs on your arm. If hair suspended above your skin is being "caught" by the razor's edge, or is lopped off on first contact, then congratulations.
Have fun.
Sam