What is easiest way to remove old varnish from old hardwood floor?

You would need a commercial sander machine. However, you will also need various grades of sandpaper, both for the machine and manual use. First, carefully remove all baseboards. Take care using the sander near walls. With the machine, you begin with the bigger grain sandpaper-- it sort of blasts through the toughest varnish and stain. You switch to a finer grain then, so you don't destroy the wood. You'll need to do manual sanding or with a handheld sander along the walls and corners or edges. Always work from higher grain to finer grain sandpaper. When down to bare wood, you would sweep with a broom (and let the dust settle), then put a buffer pad on the machine to remove fine dust. You must get up all the dust before re-staining and re-varnishing.

You MUST repair knotholes, cracks, chinks, or blemishes before going further. They make products now that will fill in scrapes or gouges, BUT you will need to let these spots dry, then lightly sand them to be flush or equal to the rest of the floor.

You'd next wash the floor using plenty of clean water--- take care to wring the cloth and don't make the wood too wet. Without stain or varnish, old wood will swell if too much water. Let the floor dry completely (use fans) and let it sit a few days till thoroughly dry. Then, you can begin staining, starting at the corner furthest away from the exit door or doorway. If you stop for a break, complete a full board first---and keep your break very short. Feather in stain between where you left off and where you apply new stain. Keep your brushstrokes even, with an evenly applied coat of stain. LESS is always better until you know how dark you want. It never looks exactly like seen on the can. If you apply another coat of stain, you'll need to let the room fully dry first, then lightly sand, sweep, buff, rewash, and re-dry as before, then do the new coat. Varnishing is fairly the same, except varnish gets tacky so you really need to work quickly, cleanly, without too many breaks. After several days of drying (curing) the floor needs lightly sanded between varnish coats. Re-swept, re-washed, re-dried... and same process all over again. My dad used to apply 4 coats of varnish. As you can see, this project is not for the faint of heart!