Puppies usually begin fully drinking milk and water from a bowl around 4 to 6 weeks of age which is around the time they're weaning off their mothers milk.
You can start introducing puppies to a bowl of milk by age 3 weeks but it can take a little time for the puppy to get fully used to drinking the milk from the bowl.
They puppy may still feed off it's mother until around 4 or 5 weeks but after that the puppy is usually drinking milk or water from a bowl.
The puppies will usually eventually learn to drink milk and water from a bowl by watching and seeing their mother do so as well.