I use human nail clippers (the big toenail kind) for trimming everyone's nails in my house, and this includes one of my cats, both ferrets, and myself. The other cat doesn't have front nails, and I don't bother with the back ones. I've found that the best way to approach the situation is to catch the cat when it is sleeping, expose one claw at a time, and clip off the part of the nail before the pink quick. Much easier than the ordeal I go through with one of my ferrets! It's pretty easy to do- just note where the pink portion of the nail starts, and clip so that you don't cut that portion and cause pain to the kitten. Start with just clipping the very tips off, and you will be able to clip closer to the quick as you get more experienced. I haven't ever clipped a 3 week old kitten's nails, but I started doing Stella's when she was 6 or 7 weeks old.
I really have to disagree with others that use human nail clippers. I suppose it might be okay on an adult (but even then cat clippers are better) but a kittens nail is just too tiny. I like these because they are so small and really let you get in close. The cutter is curved to the shape of a cat's claw and, because the handle is so short, you have really good control and it helps prevent slipping and accidentally cutting the quick. I worry with human clippers that you don't have enough control and can easily slip if she moves. And, because they aren't curved to the shape of the cats claw you risk splitting the nail. These small clippers cost around 5 bucks and are super worth the investment. I use them on kittens and adults and would never use anything else.
You really only need to take the tip off to get rid of the sharpness so don't try to get it too high. That said, I've struggled to cut kittens nails younger than about 6 weeks. They are just so tiny! If you do it make sure someone else holds her to try and keep her still. Then just flex out one nail at a time and just do the very tip. If you do accidentally cut the quick (the pink part as already mentioned) then get some tissue and apply pressure until it stops bleeding. It happens and it's not something to be super concerned about but fair warning it will bleed a ton!