When cleaning windows, you don’t have to buy a special window cleaner unless you just want to spend the money. The best way I have found to clean windows is with vinegar and warm water and using newspaper instead of paper towels.
The normal dilution is 1 cup of vinegar to 1 gallon of water. If the windows are really dirty then you should use 2 cups of vinegar.
When wiping the windows with the newspaper do one side of the windows up and down and the other side of the windows from side to side, that way if one side is not clean you will be able to tell which side it is.