if it's a good piece of furniture I'd recommend a liquid stripper first and a light sanding as well as a primer. If the piece is worth redoing it's worth doing right. That insures no peeling of the new paint and no paint filled corners etc which happens when you can't get all the old paint off. This only take an extra couple of hours and is well worth the professional look you get.
It's pretty easy. Lightly sand the whole piece. Don't worry about sanding every inch, but sand as much as you can. Then wipe or dry brush all the sanding dust off. Then paint on a coat of primer, something like Kilz. Then put on two coats of paint and you are done. I'd recommend using acrylic/latex paint. You can paint it solid or with a design or any decoration you want. You can put a clear coat finish on it, but you don't have to. You can also find books at the library or websites about how to paint furniture too. Have fun!
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