1. Turn off your laptop or LCD/LED Monitor :
Remove any power source such as power chord to avoid the electricity flow.
2. Create Your own Cleaning Solution.
You can simply use plain water, but it is better to mix it with organic solution such as vinegar. If you worried about the vinegar smell, replace it with perfume . (I always use perfume, just make sure use a very small amount, you don't want to work with strong smell, trust me!).
3. Remove Dust by using Dry Lint and Brush.
First just wipe your screen without solution, just use Lint, and then use paint brush to remove dust and clean the screens' edge.
3. Use Lint-Free Cloth or Your old T-shirt
It does not really matter what type of household item your want to use to wipe the LCD or screen, just make sure it is smooth and do absorb water. Apply a small amount of water or solution we created, make sure it is not too wet. I prefer to use empty spray bottle, the wipe your screen gently. (don't use excessive force to wipe because it could damage your screen pixel).
4. Final Touch
Again by using dry Lint Cloth wipe your screen again to remove any excessive solution/water on your screen.
I'm not a very careful guy, normally I just spray some water and let it there for 1 minute, then wipe with my old towel. I did this for about 7 years for both my laptop and my LED monitor.