All lizards do shed their skin. It is different than a snake in a few ways, and actually the limbs make it more difficult. In most species it goes in pieces, or segments. Instead of one whole strip. The toes are especially vulnerable. As is the tail tip in some species. If the shed doesn't come of, a toe, foot, or tail tip, and is left for an extended period, and another shed cycle starts, that area may not shed again, the dead skin can harden, cutting of blood circulation in the appendage and the tissue will start necrotizing, normally resulting in the toe, etc, falling off. I have taken in a number of beardies as rescues with this problem, unfortunately it is common if owners don't learn what to look for. I have a golden tegu that I took in, and we decided to keep, who is missing a toe and has a few deformed toes, from repetitive bad shedding on her feet.
Again, depends on the species. Once a section is ready to go, it normally pops right off rather quickly. For an adult bearded dragon, the whole process can take a few weeks. First the front legs. Then the head and neck. Then the tail. Then the back legs. Then the back. Though it is not always in a specific order.
If the animal hasn't had the proper moisture or humidity, depending on the species, when the skin rolls down the foot and the lizard tries to rip it off, it can rip at the top of the toe, and then the toe bit doesn't come off. Then the toe keeps growing, the dead skin stuck on doesn't.
A few weeks to shed the skin? That is much longer than I expected.
My freshwater shrimps can molt in 5 minutes, and they just apparently jump out of their old shell at the end of those 5 minutes. Then their entire old shell would just lay there like one entire shrimp but with the near transparent white color. Quite clean and easy.
It sounds awfully painful for lizards to shed their skin.
Well, it's not all ready to go at the same time. It isn't like it all gets dry and opaque at once, and then off in sections. Each section starts and finishes in it's own cycle. For a snake, the whole body starts at once, and then comes off like a sock. For most lizards, it's like a bunch of gloves, coming off individually.