You should always check your manufacturer's instructions
when determining how to clean your laptop screen.
However, here is a method that should work for most screens.
You'll need two lint-free microfiber cloths;
some water -- filtered or distilled
is best to avoid streaking;
distilled white vinegar.
First, turn off your computer and let it cool down.
Use a dry lint-free microfiber cloth
and gently wipe away any dust and smudges.
Apply gentle pressure if necessary.
If any other marks remain,
lightly dampen your cloth with water.
For glass-coated screens,
you can use a mixture of equal parts water and vinegar.
For LED or LCD screens, use only water.
Be sure to wet the cloth first,
and never put liquid directly onto the screen.
Carefully wipe the screen from left to right
in broad strokes from side to side.
Finally, polish with your second clean dry cloth
and let the screen air-dry.
If there are any streaks left,
buff them gently with the cloth.
Make sure the screen completely dries
before turning your computer back on.