Depends on what you are after as an end result, but re-polishing an antique can decrease its value, so take care. A piece in good condition, with its original finish is much more valuable than one that has been stripped and re-polished, or badly cleaned up.
The advice about warm mild soapy water & a cloth is good. Use a soft bristle toothbrush for crevices. Start on a really inconspicuous spot & test to ensure you are not going to wreck the existing finish. Wipe off moisture as you go - don't let it sit. If this does not get all the muck off, you can carefully use turpentine to loosen & remove wax buildup on just about any existing finish without damage, but again, start carefully & test. Use an open weave cloth or pieces of hessian.
Polish with a good quality paste wax -
check this out as a good example - it is used by the British Museum.
Have fun :U