How many times a day should I feed my nursing american pitbull in a day to ensure that she is receiving enough to keep her healthy and to make sure she produces enough milk for her four puppies?

Feed her 3 times a day, by feeding more often at regular times it will ensure a regular supply of milk.
She will need to be fed puppy food as well as it contains a lot more nutrients than regular dog food and will be passed on to the pups through the milk.