Depending on your Papillon's activity level, dogs of this breed don't need bathing too often. In general, a Papillon bath will only need to happen every three months or so--unless, of course, the dog gets especially dirty or stinky and an "emergency bath" is called for.
It's important when bathing a Papillon to use canine shampoo and conditioner. The kind made for humans has a different pH, and will easily irritate your Papillon's skin. Some owners like to use a 2-in-1 shampoo/conditioner combo. The best shampoo for Papillons includes brands like Earthbath, Pro Pet Works, and Paws & Pals, all of which have separate conditioners (or 2-in-1 combos).
How to bathe a Papillon: first give the dog a good brushing. Your Papillon is small enough to bathe in the kitchen sink; otherwise, a bathtub (hopefully with a spray nozzle attachment) or an outdoor plastic pool using a garden hose is fine. Wet the coat thoroughly, then apply a small amount of Papillon shampoo to the dog's back. Lather well, working downward and outward as you go. (And don't forget the legs, underbelly, and tail!) Clean the dog's face, head, and ears with a washcloth, then rinse the coat completely. (If using a separate conditioner, repeat the entire process with that.)
Towel-dry the coat, then continue with a hair dryer on its lowest heat setting, brushing the hair out with the pin brush as you dry. Finish with another quick brush-through to make the coat look clean and neat.