Welcome to the forum, caz!
Cats claws can certainly be trimmed. I would recommend waiting until she is in a very calm, sleepy mood before trying to do any trimming. You might have to just do a little at a time until she gets used to it. Some cats don't mind it, others really don't like it. Just depends on the cat
It sounds like she is a young kitten, so the earlier you start the better, to get her used to it.
Enjoy the forum!
Trimming the claws are a breeze when the cat has settled in and feel comfortable with you. Play with its paws to get it used to you touching its feets and when the cat is sleeping on your lap you can use the time to trim the claws. There's special trimmers, but regular nail clippers works as well. Just watch out for that pink pulp... rather clip a bit less than too much and do it once a week. That's what I do with my two wild ones.
OH, and WELCOME to the forum!!!!!! Never hesitate to ask ANY questions. The people here are great and you'll learn loads of stuff!
Ditto what others have said. Be VERY careful not to cut into the "quick" which is the pink area of the claw, or it will hurt your cat and there will be lots of bleeding. The best way to avoid that is to not to be too greedy and cut too much, just the little sharp tip. You may not be able to get all the pawsies at one time.
Caz, it's great to have you with us. You already have some great advice. The only thing I would add is that it might be helpful to massage her paws gently between the pads, making the claws show, as a loving gesture. That will help. She should get used to having her front paws handled especially, because they are the first means of defense.
I hope you'll post often. We need more members from Bonny Scotland!