Cleaning your screen the correct way depends on what type of projector screen it is.
Step 1: Dust the screen using a can of compressed air. (This step should be enough for most most cleanings)
Step 2: Use a new dry microfiber cloth and gently wipe the screen. Do Not Scrub
Step 3: Make a mixture of 95% warm water, 5% dish soap
Step 4: Moisten the microfiber cloth but don’t soak it
Step 5: Use light pressure to rub the screen from side to side using the dampened rag
Step 6: If the mild soap and water solution doesn’t work you can try using denatured alcohol with a microfiber cloth
Step 7: After cleaning with the damp rag pat the surface with another towel and dry the screen
Some other guides suggest wrapping masking tape around your fingers and dabbing it on the screen but manufacturers like Draper and Da-Lite do not recommend doing this as it could damage the surface.