There are two schools of thought on removing flooring polyurethane from your hardwood floors. The first is old school: an orbital floor sander, lots of pads, dust and dirt. It will remove not only the polyurethane, but also a good ¼-inch or more of wood material.
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The second—and better—way of handling this project is to visit your local home goods or hardware store and find polyurethane remover. It will be in the flooring section, likely near the varnish. You will need a special mop or special roller to apply it. You will still need to sand a bit, though not as much as you would when using the standard method.
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