For the easiest and cheapest way to get your mirror clean, dilute white distilled vinegar with water, and put the mixture in a spray bottle. Spritz your mirror and wipe it off with a newspaper. When you're done, the paper can go straight into your compost, so this method's not only cheap, it's eco [1] as well. If you're not big on cleaning with newspaper, you can also try using microfiber cloths [2].
Source [3]