There are many, many posts here on the Forum regarding cutting cavy nails. Just use the search box on the upper right.
I don't believe in the "cut a couple of nails a day". I do everything at once and get it over with for both the piggy and me. I cut them without any assistance and yes, they scream like they are being tortured! I had a female who was "Papa's girl and I had to cut her nails when he wasn't home.
I'm right handed, so here goes. Roll the piggy up in a hand towel with head covered because you are going to do the back nails first as they are the most difficult to do. Lay the piggy on your lap with your left forearm securing her against your abdomen. Clippers/scissors in your right hand, pull one foot at a time out of the towel with your left and VERY securely hold that toe. I say VERY securely because the piggy will forcefully attempt to pull the foot away. You are going to cut just beyond the quick (vein) to avoid causing pain and making her bleed. Not difficult with white nails, but if they're black, then this is a bit more of a challenge.
Use the small scissors that encircle the nail vs. human clippers. The small pet scissors will be less likely to splinter the nail. Now here is the "trick" to not cutting too short: Put the clippers on the nail and close them with just a little pressure on the nail. If you are too close to the vein, the cavy will likely whimper or squeek loudly. Reposition the scissors a little farther away and try again. If no loud protest, then cleanly cut them. Should you make a mistake and cut into the quick, it looks worse than it is. There are a variety of preparations you can use including quick-stop, cornstarch, flour, and yes, sustained pressure until the bleeding stops. You will feel worse than your girl!
The front nails are a bit easier. Now pull the towel down a bit to expose her head and so you can access the front feet.
Before you begin this phase, put on some gloves (suggest nitrile) because even the tamest cavy will be apt to bite.Position the girl in a semi-sitting position with her back against your abdomen. Still with your left hand, expose one foot at a time and using the same technique, cut the front nails.
Finish the pedicure session with some cuddles and a treat. Some cavies never get accustomed to the routine, and others come to not mind it so much in time.