Just as you'd spend the additional time to prep your space before starting a painting job, a little prep before washing your windows may lower the amount of scrubbing you'll need to do.
Before breaking out the cleaning solution, break out the vacuum -- if you have an apartment-friendly, space-saving handheld vac or a dusting-brush attachment, now's the time to put it into action. Vacuum (or sweep) all around the window, including the corners, the screens and the windowsill. While vacuuming won't help clean up water stains, mineral deposits, and dirt from the glass, doing so will help keep dust and debris that's built up around the window frame from streaking (or worse, scratching) the window glass as you clean. Use a cotton swab that's been moistened with a little white vinegar to clean any grime hiding out in corners.
If your apartment windows have blinds or drapes, take them down before cleaning -- and maybe give them a good vacuuming, too.