The first step toward refinishing your floor is to strip the old finish. While this can be done with solvents, such as mineral spirits or varnish stripper, it is recommended that you sand the floor instead. Even if you do use a solvent, they typically only remove the wood sealer and leave behind most of the stain, so you will have to sand the floor anyway. Skip the solvents completely and sand the floor with an orbital sander with a 100-grit sanding pad, then sand it again with a 200-grit sanding pad. The first removes the finish and the second smooths the wood's surface.
At the very least, you will need to remove all of the sawdust created by sanding the floor. Although you can remove the bulk of the dust with a vacuum, you should run a damp cloth over the entire surface to remove any stray dust. If you happen to notice any grease or oil stains that may have penetrated the wood, you should also scrub the floor with a solution of trisodium phosphate -- dilute the cleaner as directed on the packaging. Rinse the floor and suck up any excess liquid with a wet/dry shop vac.
When applying stain to a floor, there are certain methods you should use to make the project run more efficiently. It is usually best to work with a partner. One person will be on staining duty, and the other will follow along with a clean dry cloth to wipe up excess stain. A 2-inch paintbrush is generally recommended for staining corners and edges. The rest of the floor should be tackled with a roller or paint sprayer for maximum coverage.
Polyurethane is one of the most common wood sealers, but it's also one of the most toxic. Don't be deterred from using it, though -- as long as you follow the safety practices carefully you shouldn't run into any problems. Ensure that the room is well ventilated and everyone is wearing gloves, goggles and face masks. Unlike stain, you must use a special foam or lamb's wool applicator -- available at most hardware and home improvement stores -- to apply polyurethane. The polyurethane can be poured directly on the floor, then spread as thinly and evenly as possible with the applicator. Multiple coats, usually between three and five, are recommended for most hardwood floors.