You want to have a pet nail trimmer (reptile/bird if possible) to cut the nails since human clippers can cause animal claws to splinter. When you look at the nail, you'll see that the tip is clear inside while there's a dark/red line running from the toe. This line is the quick and is the nail's blood supply. Make sure not to cut too closely to the quick or cut it itself, since the nail will bleed. Only cut the area before the quick, leaving enough nail so that the quick isn't exposed. If you do cut too close and the nail bleeds, you can use powdered cornstarch to stop the bleeding. Just lightly wrap the lizard in a towel so that it's restrained but you can still move the towel to get the feet. The towel will help calm it down a bit since nail clipping scares most animals. Doing this when they are very sleepy works well too, since they are less likely to struggle and are calmer.
Diagram of a lizard claw so you can see what I was trying to explain. Hopefully this helps.