Before you can refinish a floor, you have to strip the old finish. This is most commonly accomplished by sanding with a floor sander. You may also consider using handheld power sanders for corners and edges. In any case, orbital sanders are typically the best tools for the job because they will conform to any contours and unevenness in the floor and gently smooth them out. For best results, two passes are generally required: one pass with 100-grit sandpaper and another with 220-grit sandpaper. The first effectively strips the finish, and the second smooths the surface.
Your floor will end up covered in dust as a result of sanding, so you will need to remove the dust before you can restain the floor. A push broom is best for removing the bulk of the dust, but you will need to take extra measures to make sure you get every bit of it. A tack cloth or damp rag will give the dust something to cling to, which ensures that the floor is perfectly clear of debris. Make two or three passes with a tack cloth or damp rag to gather all of the dust.
You generally have lots of options for tools when applying stain to wood surfaces, but you will want to stick with tools that make the work go by faster. Of course, the edges and corners should be tackled with a brush, especially if you have baseboard heating. Sprayers and rollers will make the job go much faster, but use whichever tool with which you are comfortable. Work with a partner -- one person should apply the stain and the other should wipe the wood with a rag to soak up the excess stain. Always work with the grain of the wood.
Polyurethane is one of the most common sealers for wood floors, prized for its durability and longevity. With polyurethane, you should always use a special foam or lamb's wool applicator. These are sold in most hardware and home improvement stores. Some come with long handles, making them look a lot like foam squeegee mops -- these are ideal for sealing wood floors. Working in sections, pour the polyurethane directly onto the floor, then spread it thinly and evenly with the applicator. Overlap each pass with the applicator by at least 1/2 inch to make sure you don't miss any spots.