I don't understand how to use S-Hook clasps. Am I supposed to separate one of the S's so that the ring will slide on and off? I purchased one, but the S is too tight on both sides to slide the jumpring on and off.
Yes, you have the right idea. Gently move one side of the S-hook open enough that you can slide on the end of your cord or chain; tighten it by squeezing it back into place. Attach the other half of your design to the jumpring. Open up the curve of the S-hook on the jumpring side to put the necklace or bracelet on and off.
Some S-hook clasps have two jumprings, one on each half of the "S." Use the jumprings to end each end of your design. Then open and close the S-hook accordingly to take off and put on your necklace or bracelet.
There are many S-hook clasps to choose from, select one that suits the style of your finished piece.