Every part of your baby is growing fast, including her fingernails. It’s a good idea to trim or file them several times a week to reduce the risk of her scratching herself. While she’s sleeping is a good time; you might also try after a bath when her nails are softer. When you trim, press the finger pad away from the nail, use baby clippers or scissors to cut along the curve of her fingers and file the edges smooth with an emery board.

Source:
“How to Trim Your Baby's Nails,” updated: March 2007. http://www.babycenter.com/0_how-to-trim-your-babys-nails_10027.bc