Dirty windows = dark rooms. If you live on a second floor or higher, it's basically impossible to clean the outside of the window... That is, unless you have a squeegee. You'll need to buy a soft cover for the squeegee to really get the windows clean but that's a small price to pay for natural sunlight.
Rub warm soapy water all over the windows with the squeegee, and then remove the cover to pull the squeegee across the window from top to bottom. The soap will come right off! Dry off the squeegee after every pass and only move in one direction so you aren't pushing the dirt around. Learn more here.
Get the squeegee and soft cover from Amazon for $12.