Dirty panes are no problem when you use rubber-edged squeegees, which are quicker and more effective than cloth or newspaper. They come in a variety of sizes — and a screw-on extension will let you reach high spots.
To start, dip a sponge into a bucket of warm water and a few drops of mild dish soap. Wet window; rub dirt away. Dampen squeegee; starting at an upper corner, draw it down pane from top to bottom. Repeat, overlapping strokes and wiping rubber edge with sponge after each stroke. (For large windows, ”snake” squeegee back and forth; then touch up edges.) Dry windowsills with a cloth