I think the key is to turn the device off immediately, so it's worth knowing how to do that. On a laptop/PC, one presses and holds the power button. Not sure how to do that on an ereader.
Edit: on my Onyx, it's press and hold. It then offers three choices or reboot, shut down etc. Hopefully I can hit that OFF and the screen works when its wet
A friend of mine's cat spilled coffee on her laptop. Wisely, she shut it down. Unwisely, her husband decided later to try turning it on. Bzzzzzz.