The best thing is to always have something handy to distract their biting - with lots of growing children, I used to make 'thingys' out of a pair of outgrown or holey socks simply knotted together in the middle ... Puppy always wants to chomp on something, so let it chow down on its own toy and not your arm or fingers !!
They are not nourishing or fattening and can't be confused with a treat - they are just a substitute for what puppy wants without the gratification of giving you tribal scarring !!
This will quite possibly go on until puppy is 18 months + and the sooner you make them know that mouthing on you is 'not on' the better all round !!