I wash mine in a bucket with warm water (cold water is fine if warm water is not available) and Ivory soap. I stick them in, scrub them a bit, and then rinse them off. To dry, fling them about a bit to get the water to spray out, and then leave them bristle-up in the sun. I personally only have synthetic bristles, so if you have any natural-bristle brushes, I'd double check for care instructions before cleaning them with soap...
Ivory soap is a very mild soap, so I feel comfortable using it, but I wouldn't recommend using another dish soap. :)
The hills were bathed in moonlight, the shadows not so stark;
Silver light reflected off his brown hide as he held me in the dark
– I love you, Mudpie!