Yesterday I used my glasses cleaner spray as well as thin fibre cloth to clean the screen then I noticed black marks on the cloth. Can I know why this happened and how should I clean the screen?

Water is all you need. Apple do say this. Turn off the computer, cover all other working parts and with the dampened lint free cloth, polish the screen. The exact amount of pressure is irrelevant, polish until the marks are removed. Using a spray of any kind is a No No.

As per this article : Cleaning your Apple products - Apple Support

The materials used to make Apple products vary; in some cases, each product might have specific cleaning requirements which vary by the part you're cleaning. To get you started, here are some tips that apply to all products:

• Use only a soft, lint-free cloth. Avoid abrasive cloths, towels, paper towels, and similar items that might cause damage.
• Unplug all external power sources, devices, and cables.
• Keep liquids away from the product.
• Don't get moisture into any openings.
• Don't use aerosol sprays, solvents, or abrasives.
• Don't spray cleaners directly onto the item.

In typical style, the whole paragraph of information on cleaning Apple products' screens was a "WHAT NOT TO DO" rather than what "TO DO". The only suggestion Apple provides: use of a "soft lint-free cloth". There were no specifics, i.e., how much pressure to use nor how to actually clean the screen for a clear viewing. Tried a "Soft Lint-Free Cloth" but it did not remove the multiple tiny raised spots that accumulate on all computer screens.😠

I doubt that a specific pressure rating (ie 3lbs per square inch) would be useful, common sense is what should be used in its stead.

Did the spray remove the black marks. I ask this because some types of fault on a screen can leave this effect. Otherwise, while all are important.the key part of tygb's reply is the advice not to use a spray.