When cleaning inside windows, start with the windowsills and frames rather than with the glass -- this will keep any dirt, dead bugs or other debris that may be stuck in corners from adding more smears to the mix when you begin to clean the window glass. Just spray these areas with a general purpose cleaner, wipe them clean, and dry them with a clean cloth. Good ventilation and well-controlled humidity levels in your home will also help keep windows clean; the less condensation that builds up on panes means you're less likely to see small black mold spots on your sills.
With clean sills behind you, it's time to tackle the windows. Working one window at a time, apply soapy water to each window with a lint-free cloth to loosen up the dirt and debris. (Although some may prefer a store-bought window cleaning solution, just a few drops of liquid dishwashing soap mixed with warm water will get the job done just as well.) Remove the soapy solution from the glass with a squeegee, and buff windows to a streak-free dry with a clean, lint-free cloth. Dry any drips on sills or floors with a clean, dry towel.
Regularly cleaning your screens when you clean your windows will actually make the job quicker and easier, so don't skip this step when you clean your window glass -- you'll not only eliminate heavy build-up, you'll also probably find yourself finally making that quick repair to a rip in the screen fabric you've been meaning to get to. Remove dust and debris from screens from the inside with a quick pass of the vacuum fitted with a drapery brush attachment. Alternatively, you could wash them with soap and water -- outside. Be sure to mark which screen belongs in which window before you pull them out for a soapy rinse [source: Pella].