I went real slow, especially with Pebbles (she had been messed up by a groomer with her other family). I started out by just holding the drill by the girls with it on, not trying to touch them or anything. Letting them be curious & get used to the noise. Then with it off - I started bringing it closer & touching them, laying it by them, etc.
Then, by following this site below, I began to do Lucy's nails with ease. I am still working with Pebbles slowly. I keep their hair on their paws trimmed real short, to avoid any chance of catching the hair in the tool.
How to Dremel Dog Nails @ DoberDawn.com