Haze on your car's windshield can be caused by oil or grease that bonds to the windshield, making it difficult to remove with just water or light cleaning. In order to fully remove this haze from your car's windshield, you have to thoroughly wash it with an alcohol-based glass cleaner and dry it well to avoid any streaks.
Spray the paper towel liberally with window cleaner.
Wipe down the inside and outside of the car's windshield with the paper towels. Spray fresh paper towels once the first set is soiled. Do not use the same paper towels if they are dirty.
Wipe the windshield dry, inside and out, with wadded up newspaper. Do not leave any wet streaks on the glass or they will show up later. Avoid touching your car's upholstery with ink stained hands after you dry the windows.