You yourself can clip her nails or you can bite them off. It's easiest to do when she is sleeping or feeding.
It's safe to bite them off... at least that's what my family does and it doesn't hurt the baby. Go to walmart or a similar place maybe even a dollar store and buy the no scratch mittens.
The nails are still fused with the skin on her fingers. That's why they make the little baby gloves. Give it a couple of weeks until you clip them
The hospital won't do it because the nurses are busy with more vital patient care. Also because it's really easy to snip those teeny fingertips and they aren't interested in being sued if they accidentally draw a bit of blood. Also because they want parents to learn how to do it themselves.
They are attached to the skin on her fingers. Get her some gloves. They sell them in the newborn section