So first we'll start with the warnings:
1) This instructable includes using a pencil tip being placed directly on the screen, if you are not certain you can perform this action safely then please DON'T do it.
2) Screen cleaning, ALWAYS spray the cloth you are using NEVER directly on the screen itself.
I assume no liability if you damage your screen, if you follow the instructions to the letter, the chances of damaging your screen are very low.
Having said that, let's begin...
Step 1: Clean the screen
Mix the vinegar and water in a spray bottle, (you can use it to clean windows too)
NEVER use a paper towel to clean your screen, paper products are made of WOOD, a miniscule piece of wood is enough to permanently scratch your screen.
Spray the cloth until it is damp, not soaked with, the vinegar water mixture. Use a light pressure and circular motion to wipe the screen, wipe dry with another piece of (dry) cloth.