If you only wash windows once a year or less frequently you probably want to tackle this job with more than a bottle of Windex and some paper towels. Below is my method and some tips to get you going.
My method is a 4 step process. Keep some windows open when doing this as it can get stinky.
I start by washing the window with warm soapy water to remove all the excess grime. I use a soft cloth and even get the window frame and the gunky track area. Using an old toothbrush for the track is helpful. You might want to wash windows with one cloth and keep another for the dirty track area so you aren't picking up dirt and potentially scratching your windows.
Make sure when you are done that the "weap holes" on the outside are free of debris. These are the little holes on windows in the corners that allows water to drain off outside.
Then I spray the window with full strength amonia and wipe clean with crumpled newspaper. This removes any remaining grime, grease, etc.
Then I spray the window with full strength white vinegar and buff dry with crumpled newspaper. This removes any streaks and leaves a nice shine.
Then I buff the window to a high shine removing any lingering streaks with more crumpled newspaper.
I always wash and make any needed repairs to my screens when I do the windows. I take the screens into the bathtub (put towels down to not scratch the tub) and gently scrub with a brush and soapy water, wipe the frames, rinse with the shower attachment and dry with a towel. I've heard that the spray Scrubbing Bubble bath cleaner product works great on screens. Just spray, let set and rinse clean. I'm too cheap for that and just use soap and water and a little elbow grease. Ideally you would want to wash screens outside with the same process and a garden hose. It's much easier and you don't have to worry about getting water everywhere.
Another word about screens: make sure you know which window they came from so you can put them back correctly. An easy way is to number your screens with a permanent marker on an outside corner so your storm window will cover it. Start at one point in your house and number them all in a row. Just don't forget which window 1 was and you will be fine.
Here are a few more tips that will help you:
Have all your supplies ready before you start.
Wash the inside of the window wiping horizontally and the exterior vertically. This allows you to see which side of the window still has streaks.
For interior windows, put a towel down on the floor and immediately wipe up solution or water from the woodwork.
Wash windows on a cloudy day because the sun can dry your solution before you get to polish it.
Wash a window from the top down to prevent drips.
If it's been awhile since you've cleaned your windows, it might be helpful to vacuum the frame and track to pick up loose dirt and cobwebs before you start.
If you are using newspaper wear a pair of cleaning gloves to keep the newsprint off your hands (it doesn't affect the window).
Remember that you don't have to clean all your windows in one day. Break the task down into more manageable pieces such as all 2nd floor or one side of the house. I know this isn't a really fun job. But think of how beautiful your space will look with the sun shining in sparkling windows.
Do you have a favorite window washing tip or method?