Get a cloth(preferably 100% cotton like a shirt) and wipe your screen. Make sure it's been off for a few hours before doing it so the screen is cold. Colder water doesn't run as much as hot water so there's a slightly lower risk of pushing on the screen with the cloth making the water go deeper.
Alternatively you can try unplugging it and leaving it in an air conditioned room, or at least next to a dehumidifier(but don't put it right in front of the monitor or you'll fry something by accident). The idea is that dehumidifiers and air conditioners can speed up the evaporation process. Unfortunately this will take days depending on how much fluid seeped into the screen.
That or you can just resort to a large scale rice trick(I know, that's a lot of rice). It will attract asians to fix your devices for you(okay sorry bad joke). Lay your monitor down(preferably in an orientation where the screen faces down so the water drips away from the electronics side) flat on some rice. If you haven't thrown away the box for the monitor you can probably fill that with the rice. Cover any screwholes or crannies where rice can get stuck on.
Just going to mention that I'm not an expert here and that I pretty much just summed up most replies answered by people in similar questions asked elsewhere. The only thing I really know is that you shouldn't turn it on anymore until it's pretty dry.
Ouch. So the surface is dulled and pitted rather than having had any moisture or product go under the surface, right? You might want to to try this product: www.walmart.com/ip/Displex-Cla… - note that I have never tried this one and cannot vouch for it. Otherwise, try using a *very tiny* amount of toothpaste (not gel, the 'whitening' kind is better) with moist (not wet) cotton balls. Set the monitor face-up, flat on a table, disconnected from power. Scrub with a circular motion, not too much pressure - work slowly and check the progress regularly. Hopefully, the cloudiness will disappear. Finally, clean the monitor, lightly scrubbing with moist paper toweling and just one drop of dish-washing liquid. Repeat 2 or 3 times with moist paper toweling without anything else added to remove all traces. Good luck. You can also dry-polish it at the end with cotton balls and light pressure.