I have 10 week old kitten and have had her for about a month now. She was rather calm for the first week, but after that, all hell broke lose.

Anyway, our kitten likes to bite at pretty much anything that moves -- from our feet, to our faces, and even our lips when we eat.
Usually, when she does this, we do something to let her know it is not ok. Generally, this means, removing the motivator and not our kitty (Lola). Lola loves to be held, so if we pick her up to remove her, it isn't teaching her anything persay. We need to remove ourselves/the object (ie: feet, etc). If that makes sense. It's hardest at night, when she attacks our feet, so I usually have to wrap my feet in a light weight blanket.
As a reward, when Lola is playing right, we have a treat box. Finding a treat that worked was hard though, since most treats are made for cats -- not a little kitten. I called the vet and she said to just pick up a kitten food you do not feed her and use this as a treat (we feed Lola Blue Buffalo Kitten). Based on this recommendation, we picked up Meow Mix Kitten and put the little morsels in a Tic Tac box and shake it, put treats in our hands (generally about 3) and let her eat out of our hand.
Now, she is learning when she hears that shake, it is a reward. She comes rushing and even "paws" the Tic Tac container. The little morsels are the perfect size to fit in it and it is much cheaper than continually buying the treat bags (less than $4 for a 3.5 pound bag). She usually gets about 10 a day, which is excessive, but it is working and Lola is not overweight -- and the treats are tiny!
Lola is learning, albeit slowly, but she is learning. We also reward her when she is doing well, not neccessarily associated with play time as well.
I hope that made sense.