After working in the vet field and having bred litters, you should NOT wash a newborn pup or puppies until they are SIX weeks old. Their bodies can not regulate temperature, there are no shampoos that are gentle enough for their systems.
When Can I Wash The Puppies After They Are Born?
Unless you have a small Bath, the best place would be a sink, but make sure the plug is in and you must hand wash it, don't use human soap either, because some pets may be allergic or it may upset their fur/skin. Always buy pet products, from pets at home or other pet stores, and check the labels just in case.
A week old