In general, puppies don't need to be bathed unless they're visibly dirty or smelly. Puppies -- and older dogs -- need the natural oils in their fur to keep their coats and skin healthy. Most dog shampoos are for dogs around 3 months old or older, but you can still bathe younger puppies if need be.
Not all dog shampoos are suitable for all puppies; the label will note the age at which the product is safe for use. Puppies shouldn't be bathed using most dog shampoos until they're 12 weeks old, but dog shampoos differ, much as human shampoos do. For example, if your puppy got into something stinky, you can use a deodorizing shampoo. Dogs have various skin types, and many shampoos come in formulas for dry skin or sensitive skin, among others. Choose the right shampoo for your puppy.
If for some reason you're caring for newborn pups, you can wash them gently with a warm, moist washcloth. While the mother dog generally licks her puppies to clean them, the warm washcloth rubbed gently over the body -- particularly the lower abdomen and rectum areas -- will accomplish the same thing. Newborn puppies can't eliminate wastes without such stimulation. Other than that, newborns don't usually get "dirty," as they're not moving around or playing. When you wash very young puppies, keep them warm during cleaning and afterward, as chilling can lead to illness or death.
Too Dirty but Too Young
On occasion, a playful puppy who's still too young for shampoos may get dirty to the point where she really needs a bath. Romping in the mud or otherwise getting into something smelly or dirty can result in one cute but stinky pup. If you're lucky, you may be able to find a puppy shampoo for her age, but you can also use a small amount of no-tears baby shampoo.
Benefits of Puppy Baths
Putting a puppy in some warm, shallow water for a shampoo-less bath can be beneficial to both her and you. Breeds that require a lot of grooming will benefit from getting used to bath time at a young age. In fact, a puppy's early introduction to a bath can also benefit you, no matter what breed she is. She'll be needing at least occasional baths throughout her life, and bath time will be a lot easier if she enjoys it, or at least is accustomed to it.