You don't have to stain your hardwood floors if you don't want to. All the polyurethane does is protect the floor from getting stained and damaged -- it does not require a layer of stain to be effective. If, however, you decide to add a stain before applying the polyurethane topcoat, you will need to allow the floor to dry completely to avoid streaking and improper drying of the topcoat.
Cleaning the Floor
You can't have anything on the floor that will interfere with the application and drying of the polyurethane. Before you get ready to apply your polyurethane, give the floor a thorough sweeping and vacuuming with a strong wet vac. Once all of the dust and other debris is removed, wipe the entire surface of the floor down with mineral spirits. This will remove any oil stains that have soaked into the wood.
Preparing the Room
Open up all of the windows in the room to allow for proper air ventilation. Polyurethane fumes are toxic, so you should wear a breathing mask when working with it. Place painter's tape on any baseboards and walls that connect with the floor. This will prevent the polyurethane from coming into contact with these surfaces while you work.
Always read the manufacturer's instruction label for specific directions on how to apply your polyurethane. For the most part, you simply paint the polyurethane onto the floor with a sponge or lambswool applicator, allow it to dry, sand it, reapply and repeat two or three times. As the first application dries, the polyurethane will most likely bubble up -- the sanding step takes care of this. Again, it is imperative that you read the label on the packaging for specific information on application and drying times. Some dry in as few as four to six hours, while some take up to 24 hours to dry.