If the cats nice about it, one paw at a time, press the center to force the cat to flew the claws out (it doesn't hurt and it doesn't take much pressure) and snip the white, clear part.
If the cats not nice, it can be a two man job or a kitty burrito job (cat, towel... Sometimes ducktape helps)
Cats have clear nails, so you can see the quick. However, a healthy dog or cat cannot bleed to death through the quicks, so, if you do hit the quick, don't panic. It's really not a big deal.
Also, I've noticed that cats don't seem to notice it as much as dogs when you do hit the quick and they rarely bleed at all when you do.
I'm always slightly amazed about how stressed people get over this process. Dog and cat nails are easy. You want a challenge, try trimming the nails on a squermy rat. I'm paranoid I'm gonna take off a whole toe.