I like to clean mine with sudsy ammonia and a soft brush. I soak it awhile and then give it a little brush and rinse in warm water. Cleanings at a local jeweler every so often are a good idea. I also take my ring off and store it in its box far from the kitchen sink when washing greasy dishes, making meatballs, etc. You get the idea, I'm sure.
Diamonds attract and hold onto grease, lotion, etc.
Unfortunately, it seems that the cheap ones do a poor job of cleaning and the shaking can loosen the diamond. This is just what I've been told.