Cat restraint can be a bit tricky; as a general thing, less is more, but some cats go full-scale Defcon 1 as soon as they think you’re up to something. A lot of the trouble is figuring out what sort of cat you have. It took us the better part of a year to figure out that Eponine can be jollied along into most things, and is pretty well-behaved about the rest provided you wrap her up at the outset. If you try normal restraint and then go to the towel, she gets violent and stays that way. Put her straight into the towel, and she just lays there and howls. Cats are weird.
If your cats are pretty amenable to rubbing and petting and scratching, just let them sit in your lap and quietly reach over for the clippers (I prefer human fingernail clippers for cats, the smaller size gives you better control) and clip a few nails. You’ll probably have to break it up into at least two sessions, and you’ll have to have the clippers handy–if you carry them around hunting for the clippers, they tend to get upset and pissy. If this just doesn’t work for them, try desensitizing them. If it’s still not working, you’ll have to actively restrain them and have someone else trim the nails.
There are a lot of ways to restrain a cat, but the ones I prefer are the bearhug, the burrito, and the scruff’n’stretch. You’ll have to experiment to see what works best for you and for your cats. The bearhug is very effective for many animals, but it can take a lot of practice to get comfortable with it. For this technique, you put your hand around the cat’s neck, loosely, with your thumb and forefinger lightly gripping the jawbone and your pinky against the shoulderblade. Pull the cat’s head gently against your shoulder, so the cat can’t turn its head and bite. Put your other arm over the cat’s back so that your elbow is either against the hips or behind the butt. Grasp the foreleg in your free hand at the elbow, then pull your arm back so the cat is gently but firmly pinioned between your arm and body. If you need to, you can lean forward and use your upper body weight to press the cat down onto the table. When working on the back feet, hold both forelegs at the elbow, with a finger between the legs, so the cat can’t reach up and claw the hand you have around its neck.
The burrito method is an adjunct to the bearhug, and there are variants for differing levels of fractiousness. You can drape one paw while working on the other, you can make a cape to hold both front paws, you can wrap only the back half, or you can make a full-on burrito with just one paw hanging out. You need a large, thick towel for any of these. The single paw drape is pretty self-explanatory, so we won’t go into that. The cape is also pretty basic–you lay the cat on the towel so that it extends past the ribcage, then pull it up snugly around the neck like the capes they put on you during haircuts. For the half-burritio, you spread out the towel and put the cat on it so that the front legs are hanging off. For best wrapping, put the cat about halfway down the long side of the towel, and make sure there’s some towel extending past the butt. Pull one side firmly up and around, then the other and flip the excess towel up and over the butt, just like putting a towel on your hair. The full-on burrito works very similarly, except you put the towel in front of one foreleg and behind the other (make sure it’s good and snug behind that elbow and well up over the collarbone on the inside leg). Make sure you wrap nice and tight, with kitty’s legs folded up in a lying position and no room to stretch them out. You can also do this with just one hind leg hanging out.
The scruff and stretch is often the easiest hold to learn, but it’s often pretty upsetting to the cat, and it can make the owner feel pretty cruel. For this one, you grasp the cat very firmly by the scruff, and catch hold of the back legs with the other hand. Put your thumb and forefinger around one leg above the hock, and the other fingers around the other leg. Stretch the cat as far as it will go and lay it on its side. You may have to just do the paws on the up-side, then switch your hold and lay the cat on its other side.