Wipe each crystal piece inside and out with a damp, soft cloth. Pay close attention to grooves and nooks, wiping them with a corner of the cloth. This will remove dust and light dirt.
Mix a solution of equal parts apple cider vinegar and water. Immerse the crystal in the solution and soak it for an hour. Remove the pieces from the solution and wipe them as before with a clean cloth. White wine vinegar is a good alternative as well. Balsamic and other dark vinegars are too acidic for cleaning.
Clean all of the crystal pieces in warm water with gentle dish soap. This will remove residue from the vinegar. Do not immerse the crystal in hot or very cold water, as this could cause them to crack. Make sure the water is slightly warmer than room temperature to avoid damage.