I feel like an idiot, but I can't figure out how to make my dudes drink from the canteen. Please explain it to me like I'm an idiot, because I apparently am.

Move it to their head IIRC.

Precisely.

In the inventory screen, picku up the canteen then "drop" it on the merc's head.

Note: camouflage kits are used same way on the body. Beer is used like canteens. These are the only 3 items used in the inventory screen.

Yep, in the inventory screen you select the canteen and then you click on the silhouette's head (not the merc's portrait). Canteens are replenished at the beginning of every day so don't throw them away when you've emptied them.