Place a piece of plastic wrap on a flat surface and put the tangled necklace on top of it.
Drop one or two drops of baby oil or vegetable oil onto each knotted area. If you don't have a dropper, use your fingertip to put oil on the tangle.
Stick the ends of one or two straight pins or needles into the knot and move them around gently to loosen it. The combo of the oil and the pins should help you work out the tangle. Gently pull the tangle out once you loosen it enough to insert your finger.
Wet a lint-free towel and place a drop of mild soap on it. Rub the soap into the wet towel to create lather. Wipe the oily areas of the necklace ever so gently to remove the oil. Wet another portion of the towel and wipe the soap residue away. Allow the necklace to air dry before you stash it in storage.