If you have a heavy concentration of slurry, then you can use a Nagura stone for cleanup, and there’s a lovely walkthrough on the process at Knifewear which we’ve linked for you. You won’t need to do this often, however, as usually, you’ll just need to rinse your stones and then wipe them completely dry with a clean cloth.
After that, let them air out overnight and then you can safely store them away in the morning!