I cut Stewie's nails:
1. I put him on his back on my lap and massage his paws for a bit, then rub his belly.
2. I let him sniff the clippers and talk softly (baby talk) to soothe him.
3. I go to town as quickly and efficiently as possible!
I've made him bleed once out of the dozen or so times I've done it. Not bad for a non groomer, huh?
That one time I put some flour on it and it was fine.
Sing to your Yorkie when you're doing it and let them know that everything's gonna be great! Doing it when their sleepy is not a bad idea, either.