I've done a lot of piano refinishing. First thing you need to do is remove the action, and completely disassemble the piano. If you don't know how to do this you may want to hire a piano technician to do it, because you can break hammers off when removing the action.
Take all the hinges, and other hardware off, and put them in a jar, or somewhere for safekeeping. You may want to have seperate jars with labels for different items. It really stinks to start putting the piano back together and not have all the screws, or to put the screws in the wrong places.
I also take the legs off and put the piano onto 3 small saw horses. Just build them about the height of the legs, slide one under each section and remove the legs. The legs are held on by screws, and/or lock plates. You'll need to screw the lock plate pressure screw coming into the side of the leg, in, and then tap the back of the leg towards the inside of the piano to release from the lock plate. Sometimes you need a rubber mallet to get it to release. If you need any help removing the legs, consult a piano technician.
Now you have the piano unassembled you refinish as you would any other wood. Strip, sand, repair any holes or other bad spots in the wood, sand some more, apply pore filler, sand, and then apply whatever finish you want. Pianos traditionally have a lacquer finish but anything works as long as you've done your surface preparation correctly.
It's a hell of a lot of work refinishing a piano correctly. Really not worth it unless the piano is in decent condition. I'd get a piano technician to look at the piano before I spent that much time on it. It may have some serious flaws that aren't visible, or that you just haven't noticed yet.