I have taught several kittens

First, this is just a phase they go trough, while growing up. They will grow out of it. But if it worries you:

1) They are play fighting. Usually their kitten siblings would be their target and any "over the top" bite would be punished with an enraged meow and a bite or a paw scratch.
- Say "ouch" loudly, take your hand / foot away and ignore them after a strong bite (play bites can be ignored). If you feel up to it, do the nibble / bite but it isn't necessary. Just ending the game is good enough

2) Play a lot with your kitty: Strings, feathers, throw those little balls slowly for them... They will learn other ways to have fun besides biting

3) Even play fights are fun:
- Use your hand to mock a big monster mouth and aim for the kitty's neck (slowly and gently obviously!), do a "swordfight" with your fingers and his paw, etc... Again, stop the game yelling loudly as soon as the kitty bites or scratches too hard. You want to teach him limits.

3) While play fighting the kittens have this secret code that says "you won" or "I yield" that signals they are tired of the game and want to stop: They go limp.
- While play fighting with your kitty, if he hurts you or you get tired, make your hand / foot go limp. He should stop.
- If he goes limp, stop a bit and talk soothingly, petting him.

Soon enough you two will learn to play without hurting each other and you wll be the best of pals