Bathing a Cairn Terrier doesn't need to happen often. Too-frequent baths will strip the coats of their natural waterproof oils, and even change the coats' texture. A Cairn Terrier bath only needs to happen every few months--unless, of course, the dog gets especially dirty or stinky!
Some larger metropolitan areas are seeing an increase in "mobile dog groomers," which are work trucks that can provide a mobile dog wash for Cairns and other breeds.
If you instead choose to bathe your Cairn yourself, though, it's better to use canine shampoo, as the kind made for humans can irritate a dog's skin. Many breeders and owners say the best shampoo for a Cairn Terrier is one formulated for "hard coats." Miracle Coat Curly & Wiry and Bio-Groom Wiry Coat are two recommended brands, both of which are available on Amazon and other outlets. Conditioner is optional, but is not at all required.
How to bathe a Cairn Terrier: first give the dog a thorough brushing. Your Cairn might be small enough to bathe in the kitchen sink; otherwise, a bathtub or an outdoor plastic pool using a garden hose will be fine. Wet the coat completely, then apply a small amount of 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 your Cairn's face, head, and ears with a washcloth, then rinse the entire coat until the water runs clear.
Towel-dry the coat, then finish by giving the dog another quick brush-through to make the coat look neat and clean.