Polishing wood is something best done by hand. Soft woods take a more delicate touch while harder woods can handle a bit more abuse.
Make sure your wood is clean and dry before starting. Using 0/0 sandpaper, carefully rub the wood in an up-down motion - ALWAYS rubbing with the grain! if your wood has ridges or groves (decorative areas), make sure you get between them. Every so often, gently blow off any wood dust that accumulates on your wood also, tap the sandpaper to shake loose any dust that sticks in it.
Once the entire piece has been rubbed, use a tack cloth (or linseed oil on a rag) to remove all dust. Again, always rub WITH the grain.
Place some commercial wood polish on a clean dry cloth and gently rub it onto your wood - up and down, with the grain. Make sure you apply polish evenly to all areas. When dry, buff your wood with a clean dry cloth for a mirror-like finish.

With a woman`s ass. ;)

Stripping off as much old paint as possible. Then washing it with T.S.P a few times. Once that's done, sand paper with medium to fine paper, then finish with one of the finest grains possible. Once that's all done you have to remove all the wood dust. With a blower then a damp cloth. Finally you're ready to polish it. Get a high quality wood sealer, then use whatever is recommended for the wood the chair is made with. Just don't wax it, unless nobody will be sitting in it.

Paint stripper, sandpaper and a new coat of varnish.

A friend of mine spray paints her wooden projects in either Silver or Gold. It looks quite nice.

Is that the color of the wood?It looks like it needs a paint job.

Menzerna makes wood polishes check them out. They are good.

i hate painted wood. i think its kind of tacky

Is that Norwegian wood?