Polish with a Microfiber Cloth
Microfiber cloths excel at putting the finishing touches on mirrors, countertops, and even tile and fixtures. After cleaning surfaces with your favorite cleaning solution and drying them off with a terry cloth rag or a separate microfiber cloth, polish them to a mirror finish with a dry microfiber cloth.
Microfiber cloths are perfect for this because they pick up dust, wipe off smudges and don't shed any fibers. You'll find microfiber cloths wherever cleaning supplies are sold. You can also buy them in bulk at wholesale clubs and use them throughout your house for all kinds of other cleaning chores.
Vacuum First, Then Scrub
For a really thorough cleaning, start at the top, vacuuming the dust from light fixtures and the top of window casings. Then work your way down. And finally, vacuum the floor methodically so you cover every inch. You don't want to leave any stray hair or dust bunnies to muck up your cleaning water. A soft-bristle upholstery brush works best for this type of vacuuming. Figure out what vacuum to use here.