Summarize:

Use kitchen shears or a heavy cleaver to cut the toenails off the end of each chicken foot. If desired, you could also separate the palm of the foot from the connecting leg bone by cutting them apart at the joint. Both parts can then be prepared and cooked in the same manner. Doing this can make it easier to fry the chicken feet, but it will also change their distinctive appearance. Stir 1 Tbsp (15 ml) of salt into 1 qt (1 L) of cold water. Dunk the chicken feet in the salt water and scrub them clean using your fingers.  Rub the feet together while submerged to help scrub off any dirt or debris. Peel away any scaly, yellow outer skin. If you cannot pick away these spots, you can use kitchen shears to cut them away. Remove the chicken feet from the salt water and rinse well under cool, running water. Drain and dry the feet completely using clean paper towels.  It's very important to completely dry the feet after rinsing them. If excess water remains, you may encounter more splattering when you start frying the feet. After drying the feet, set them aside on a clean plate while you prepare the frying oil.
Clip off the nails. Wash the feet in salt water. Rinse and dry thoroughly.