Turn off the monitor--or if you haven't yet powered-up your computer--now would be a great time to clean it.
Apply a few sprays of non-ammonia based solvent to a lint-free cloth. Please refrain from spraying the solvent directly onto the screen. Wipe around the entire monitor and just give it a good "once over" for now.
Once you have applied the solvent you can now remove all the oil smudges and gunk. Don't press too hard because you can damage the monitor. LCD monitors are a little pliable and can cave in with too much pressure.
If you want to get really neurotic you can use a technique used by both photographers and maid services alike. The use of "oblique lighting" will allow you to look down the side of the monitor to ensure it now has a clean gloss.