How do you clean stains in white agate jewelry?

Take it to a jeweler. They can clean jewelry much better than you can at home. Any type of porous stone can get stains like this, such as opals, emeralds, etc, and they need cleaned and oiled periodically.

Hope this helps!

at home you can clean them by using soft cloth dipped in any oil( olive oil or cod-liver oil are best)
keep it away from dust and other hard stones.

polish it regularly with oil.