First of all, make sure to use your vacuum cleaner to clean around the edges and to remove any loose dust, dirt or even cobwebs in the corners. The more of the loose dirt you can remove now means that there is less chance to get unwanted residues smudged or smeared on the glass when you are washing it. Don't forget to vacuum around the sills also. If you have blinds installed, it is often useful to use a feather duster to remove any dust from these before you clean the actual pane.
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I learned this tip from this message board years ago - water and cornstarch solution for washing the windows, and a good quality squeegee is also a great tool to use for windows and you won't need the newspaper.

If you don't like the ink left all over your hands from newspapers, you can get the unprinted newsprint - the end of the rolls - from your local newspaper office for free/cheap. We've used unprinted newsprint paper for all kinds of things:

-windows
-kids crafts/drawing/art
-wrapping glassware for storage/moving (NO ink residue on anything)
-filler for packing when sending a package
-gift wrap

-Grainlady

I use a Norwex Microfiber cloth with just plain water and then polish with one of their polishing cloths. My windows are flawless. Best part they don't get as dirty anymore because I am not using any chemicals with residue for the dirt to attract to.