Steve has it. Zep concentrate (Home Depot), a sparayer and a squeegee. Expect the exterior to bleed paint and dirt.
1. Webster the casement.
2. Spray the windows. (I often use a hose end sprayer with bleach and car wash detergent to do a gross decontamination).
3. Light spray with Zep and squeegee, 2X.
Interior
1. Vacuum all mullions and the sills. Use a stiff brush to break up the sill deposits, a spotter to flush them if need be.
2. On wooden window frames, spritz with diluted bleach and car wash. Use a soft brush to scrub it in, your spotter to recover slops. This will restore them to bright paint. Do all at once and get the suffering over with.
3. Go back with Zep. Use a small squeegee for those damty small panes.
4. When dry, polish any dripsicles.
5. For tip-in vinyl, modify the above to suit yourself.
Accept that no matter how you try, the upper window edges will run a little. Dry wipe them later if you must. Thermopanes grow a white fungus between the glass. You cannot get to it.
Be ready to discover a zillion blems in your work, they reveal themselves as you go.
Hard water deposits call for Mr. Makita and Barkeeper's Friend. Use distilled water to rinse or you'll simply redeposit the dots.
Relax with a cup of coffee and enjoy your wife's admiring comments.