According to Dr. Sears,
- Trim your baby's fingernails while baby is in a state of deep sleep, recognized by the limp-limb sign: Baby's limbs dangle limply, and the hands are wide open.
- Use a miniature nail clipper designed especially for babies. They are much easier and safer than scissors or adult-sized clippers, and baby's paper-thin nails are so easy to cut anyway. If not using a nail clipper, use safety scissors with blunt ends in case baby startles during the cutting.
- To avoid snipping the fingertip skin as you clip the nail, depress the finger pad away from the nail as you cut. As a beginning nail cutter, have your spouse hold baby's hand while you manipulate the finger and the nail clipper. After a while you will be able to trim baby's nails by yourself.
- Drawing a drop of blood is part of learning nail trimming. Apply a bit of pressure and a dab of antibiotic ointment to the little nip.
- If you're squeamish about cutting tiny nails, cover them with cotton mittens.
I also found an instructional video if you are interested: