The best thing to do with any stone, diamond or not, is to clean it after each use. Much easier to stay ahead of it this way.
Diamond hones are very easy to take care of. I've just been using dish soap & warm water after each sharpening session. I believe DMT recommends occasional cleaning with a mildly abrasive kitchen cleanser like Comet or Ajax, with water of course. Use a scrub brush with it. Others here also like a product called Bar Keepers Friend. Need to be a little more careful with it, because it uses a chemical reaction (oxalic acid) to remove the metal fines from the hone. The oxalic acid reacts more aggressively with some metals, than with others. Be sure to read the warnings on the container very carefully.
Since diamond hones are generally made of steel plates (coated in nickel & diamond abrasive), and are therefore vulnerable to rust, be sure to thoroughly dry the hone before putting it away. Rinsing in very warm (almost hot) water will help to evaporate residual moisture away.
Another note. Some folks actually use a little bit of soapy water (w/dish soap) on the hone while sharpening. Sort of lubricates the hone, and will also help to float away much of the metal fines while sharpening. Similar to using oil on a conventional stone, but MUCH easier to clean up.