For the first few months we used to just bite our kids nails. I know it sounds weird, but one midwife and two aunties suggested this and it seems to be fairly well recognised way to do it.
If you do want to use clippers, get the ones with a buffer - this stops you accidentally cutting into the baby's skin - which is quite easy to do if they are wriggling. Also use two people - one to hold their arm still, and the one wielding the clippers should hold the finger still - or do as @Swati said and wait for baby to fall asleep.