I can tell you how I clean my microscope and camera optics; of course that doesn't mean it is the right way to do it, but I am willing to learn better ways.
I never wipe with a dry cloth or paper. I use an "ear syringe" to blow loose dust followed by a clean (non-greasy) lens brush.
I use two kinds of cleaning fluid: Zeiss Lens Cleaner (
http://www.amazon.com/Zeiss-Lens-Care-P ... ns+cleaner ) and Zippo Premium Lighter Fluid (in metal can). Zippo is great for cleaning immersion oil as well as other oils or greases (better than other stuff I tried and it evaporates very quickly). I slightly wet the cleaning cloth (see below) with the fluid (Zeiss lens cleaner or Zippo), and wipe the lens very gently (no pressure at all). For tiny lenses (microscope objectives) I wipe across the lens in one direction once, use a new cloth and repeat in the same direction until clean. For larger optics (eyepieces, camera lens) I use circular motion spiraling from the center outward; again I use a new piece of cleaning cloth to repeat as necessary.
Optics inside the instrument and especially first surface mirrors gnerally require special care and are best left alone, I think.
Cleaning cloth: I use either clean, lint-free microfiber cloth or PecPads (
http://www.amazon.com/PEC-PAD-Lint-Free ... ds=pecpads ). I cut the cleaning cloth into one inch squares and store them in a Ziploc bag, the use as necessary.