Use liquid handsoap, rub onto mirror and use the palm of your hand to move it in circles until the entire mirror is white and creamy, then use a regular hand towel and slide from left to right once , then move to the next clean part of the towel and do the next left to right strip.
Don't worry about the little white line left between strips, do these after the mirror is completed.
I usually do this each time I'm changing hand towel in bathroom. It's gives superior result compared to any other method I've tried.