... do you mount it on a wood or plastic board so it doesn't crack, and if so, how?
For a not-to-be-immersed stone my guess would be tile mastic on wood because the adhesive is rigid but sticks to porous stuff. How about stones that stay wet?
For sword polishing, some of my waterstones are sawn into very thin slices, then used by placing them on a springy wooden fingerboard. Some people glue them, some don't. I find that a coarse bandsaw blade leaves a rough enough finish on larch to not need it.
Many waterstones (particularly hard/fine polishing stones) are permanently mounted onto wooden stands. A hot hide glue & resin mix was traditional, or you can use silicone these days. If you want to take them off later, silicone can be sawn through with a bit of fishing line and toggle handles.
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