To clean a crystal chandelier, mix a solution of either one part ammonia or one part isopropyl alcohol with three parts distilled water. Both of the solutions are mild enough that they do not damage crystal, and using distilled water prevents the crystal from being pitted by minerals.
Tap water generally contains excess minerals that can harm and damage crystal and should not be used. For a light cleaning, simply spray the cleaning solution into a soft cotton cloth and wipe down the chandelier. Do not use paper towels or disposable dusting cloths, as these materials are rough enough to scratch the crystal and its fixings. Also, do not spray the cleaning solution directly onto the crystal.
For deep cleanings, disassemble the chandelier and wash each crystal by hand in warm, soapy water. Add a small amount of white vinegar and a drop of dish soap to the water to increase its cleaning power. Do not dump all of the crystals into the sink at once, as this may scratch them. Rinse each crystal off with cool water, and lay them on a paper towel to dry. Reassemble the chandelier. It is a good idea to take pictures of the chandelier from many different angles in order to have a reference when putting it back together.