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Well, the first thing to do is to set the animal up so it doesn't have this problem. There are many tricks that people have developed over the years, moist hides for leos, regular baths for beardies, having large water dishes for most monitors to soak in. Learn how to keep the animal properly, and you will rarely have to do this.
What to actually do will vary from species to species, and situation to situation. Typically you will want to soak the animal in lukewarm water. if it is skin on the body, you can peel it gently, but never peel anything that won't give naturally as you can injure the animal. You can also rub it off gently with a damp cloth. Much of this goes for snakes as well. The real problems are normally on the toes, tail tip, and eyes. That is where lizards have an extra problem. If the skin from the toes is not shed, it will build up, cutting of circulation and the affected toes will end up necrotizing and eventually falling off. The good news is that most lizard species seem to have evolved to recover from this very quickly. With retained shed on the toes, you want to soak the lizard to soften the skin. You may have to do this multiple times, depending on how long the shed has been there, and if it is multiple layers. After it is softened, you basically have to get it off, which can be a tricky proposition considering how small and fragile most lizards toes are. I have a Golden Tegu, Tupinambis teguixin, that I took in as a rescue, with multiple retained sheds on her feet. I soaked her a few times a day, and eventually clipped the skin off with a sharp pair of sewing scissors. She had already lost a few toes by this point. She was kept in a dry cage with a small water bowl. I have now had her for almost 6 months, with a large water pan she can soak in, and swim a bit, and haven't had to do a thing to help her shed.
The point being, these problems are all caused by improper husbandry. So the single most important thing you can do is to learn the best ways to keep your animal, then do these things, watch the animal for problems, then act and adjust accordingly.
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