Spray paint stripper onto the floor and leave it in place for a few minutes. The paint stripper chemically interacts with the varnish to loosen it from the hardwood floor. Make sure you open windows and doors before using the paint stripper, as the fumes that it produces could make you feel dizzy.
Now that the varnish is loose, you can remove it using a scraper blade. Alternatively, you can use a damp mop to wash away the varnish. Avoid getting the mop too wet, as water can damage hardwood floors.
Paint stripper is unlikely to remove all of the varnish. The next step is to use a floor sander with coarse sandpaper to remove the varnish that remains. Turn on the sander and move it slowly and evenly across the floor in the direction of the wood grain.
Repeat the step above, but this time using fine sandpaper rather than coarse. This final step removes the last traces of varnish and leaves the floor looking smooth.