Excruciating. The first few times, you don't even think it's possible to clip them without cutting flesh. We did it while the kid was eating, but now that she's actively involved in feeding, this doesn't work so well anymore.
You could cut your kid's nails while she's sleeping (but then you'll feel like you're risking waking her up, which would be stupid). Or you can try negotiating, asking an infant to sit still and not move. This is a fool's errand, and you will inadvertently clip your kid's fingertip. You might just catch a cuticle, or you might make clip-long incision that draws blood. In either case, she will scream with real pain, pain you inflicted, and it will make you feel like a dirty, sadistic failure. Then you'll spend several hours wondering what the long-term impact of such abuse is, and will it end up in her book?
Rather than risk this uncertainty, I suggest going with the damage we know: let the kid watch some TV. She'll be an inert zombie for at least as long as it takes to trim the nails. And we use baby-sized clippers; the scissors just feel too unwieldy right now.