From Leopard Gecko Wiki
Leopard Geckos, like all reptiles, shed. When shedding, they will turn a ghost white color. When they reach this color, the shedding will generally occur within 24 to 48 hours. To assist in shedding, a Humid Hide should be provided to the Leopard Gecko in the cage.
Shedding complications can be common, but are easy to fix. The most common shedding problems will occur in the toe and foot region. When there is excess skin stuck on the Leopard Gecko's feet or toes, there are two steps to removing the skin. First, give the Leopard Gecko a soak for five to ten minutes in lukewarm water. The depth of the water should only be enough to cover its feet. After the soak, if the excess skin still remains, a moist Q-Tip cotton swab, or your fingers, can be used to get the skin off. Gently rub the Q-Tip, going towards the toe tips. If these methods do not get the excess skin off, a local Reptile Veterinarian must be contacted. If the skin stays on their toes, over time it will become very tight, causing blood flow to stop, and the toe could fall off and/or become infected or gangrene. Check their toes regularly, and they will be grateful.
Often, when you are trying to get the skin off their toes, they will pull their foot away every time you touch it, making it difficult to get the skin off. After soaking your gecko's feet, try bending your knee up in the air while you sit on the bed. Set your gecko on the top of your knee. Then place the tip of your finger on top of the gecko's foot that you are working on. Your finger should cover most of their foot except the toes with the dead skin. Apply a little bit of pressure on their foot--obviously, not enough to hurt their foot. They seem to like this: if you do this, they will be a lot less likely to try to jerk their foot away as you carefully tease the skin off the toes with your other hand. As stated above, a cotton swab is one option. You may also be able to use tweezers--but they must not be sharp or you can hurt the skin. If you are using tweezers, you must have good eyesight to avoid jabbing or pinching their living skin. In any case, covering their foot with your finger seems to work very well, and is less annoying to your gecko.