Use a professional dog groomer.
Sometimes your lack of experience and confidence can be a part of the problem, significantly if you cut the nails too short and hurt your furry best friend.
However, a trained dog groomer will do the task very quickly and efficiently, taking a lot of the stress away for the dog. They might still get scared, but the job will be over so soon that it will not be much problem.
Make it a positive experience.
Whether you cut the nails yourself or have a professional, do it, make it a positive experience. So, they glance forget that you have just cut their nails. For example, give them their favorite food and treats immediately after. Or take them into the garden for their favorite game. Or you could do the nail clipping when you are out on their favorite type of walk,
Get them used to you touching their paws.
When they are a puppy, you should get them used to be touched and handled for specific purposes. They should trust you and allow you to do things without them trying to wriggle away. It might be a bit harder and might take longer for a new rescue dog to get used to you touching them because you do not know what they have been through.
Before you ever attempt nail clipping, you should make sure your dog is used to you taking hold of their paws and examining them. Like with all dog training, consistency is the key. Use the same commands, tones, and actions. Then build up the time you hold and examine the doggie's paws.