If you dragon will sit for it you can file them down (if they are scratching you or more importantly they are getting caught in things, like a hammock if they have one or on their carpeting, as they can actually hurt their legs from yanking them to free their nails), but if your dragon is like my 6-month old boy he refuses to sit still long enough for me to file them, so I clip them when they get to that point.
It's easy, but always good to have some corn starch or styptic powder (Qwik Stop) on hand just in case you clip too much off, as they do have a vein just like dogs do. If you look at his nails from the side you'll see the portion of the end of his nails that is like an "overhang" over the pulp, that's all you want to clip off, just the part of the nail's tip that is sticking out beyond the pulp. I just take the very tip off of the end of each one and that's it, no big deal and once you do it once or twice it's easy.