bones take roughly 6-8 weeks to heal, depending on health and age. In your puppies case it make take three months in total as unlike humans, he/she cannot be expected to rest it or cooperate with regime.
Don't worry, the cast will only be taken off once it is ready and then it will take 4-5 weeks for the mucles to fully recover.
Why not ask the vet?
When did they tell you to come back and have the cast removed?
Call them and ask.
it depends on the injure of the dog
Rayven is right, it depends on your puppy's health, where the break is and how severe it is. But when my dog (3 yrs at the time) got hit by a car she broke her leg in 3 places and they preformed surgery, and her recovery and or the time it took for her to heal was about 8 weeks. It might actually take less for a puppy, because their bones are smaller.
I don't think you have taken him to the vet, just take him to VET now! vet will take care of all this, and will give you guideance. otherwise you are trolling?
why didn't you ask them?
Depends on where the break is, type/severity of break, overall health of the pup, whether you follow all the instructions given to you by the vet as far as activity level etc.