Congratulations on the mealworms!
I'm not a mealworm expert, but I have raised quite a few in the past. You don't want to give them straight water (poured on their food, etc.), since that will soak everything and encourage mold growth. Instead, there are several other ways to give them moisture:
Apple: Cut up and apple and put a few slices in with your mealworms face down. Thirsty mealworms will latch on and suck the moisture out of the apple. Remove the apple every few days to prevent mold and give them fresh moisture.
Moistened paper towel: Tear off a piece of paper towel and dampen it with water. Then, lay it down on top of the mealworm's area. Like with the apple, they will suck the moisture from the paper towel. Re-moisten the paper towel every few days, and replace as needed (mealworms tend to tear up or eat the paper towel eventually).
I believe you can also cut a potato into slices and put the slices in with them. Once again, replace the potato slices ever so often to ensure they're getting enough moisture and to prevent mold.