I've read that after sanding, you should wipe the floor using a rag and mineral spirits before applying the polyurethane. How do you do that for a whole room since you can't rinse the dust out of the rag after every few wipes? Do I use a bunch of old towels soaked in mineral spirits? After the initial sanding to bare wood and then sanding between 2 or 3 coats of polyurethane, that will call for a lot of old towels and rags. I'm not sure I have that many old towels and rags. How is it typically done? Thanks for your help.

This type of final cleaning before the coat of finish is called tacking the floor.
I only tack the floor between coats of finish.
With the dust collection on the machines today there is not much dust left on the floor. We used to just sweep the floor, but today we vacuum with a back-pack vacuum that has lots of power, so there is really no need to tack the floor.
Tacking involves using the right solvent spread on a towel to just dampen it.
Don't use too much solvent, which may be water instead of mineral spirits, between coats of finish.
Spread the towel flat on the floor.
Set a push broom parallel to the long side of the towel about six inches from the front edge. This will be the direction that you will be pushing it.
Fold the six inch flap back over the push broom and start pushing it from one end of the floor to the other along the wall.
When you get to the end of the run, near the opposite wall, you stop about a foot from the wall, pick up the towel and give it a little shake to have the dust fall off.
Then lay the towel down to push it back to the other end of the room. Pick it up carefully and give a shake, like the other end.Work across the room toward the other wall.
When you have gone over the whole room, you will have a collection of dust at both ends of the room.
Tack one end into a pile and collect the dust with a broom , then use the towel to attract the last bit of dust to be shaken outside into a trash can.
Then clean the other end of the room.
This technique works best in a long room like a gymnasium.
You don't want to saturate the towel with solvent, just damp.
If you want to use a little different method for smaller rooms you can work like a tractor plowing a field and go into smaller and smaller circles, then push the dust toward a door.
It's important to not use so much solvent that you wet the surface. If you do you will find that the damp floor will attract dust that you are trying to collect as the towel slides by the last row that you have tacked.

Thank you for the excellent lesson on tacking. It is appreciated.