Is it okay to use micro fiber cloth and the lens cleaner that comes
with eyeglasses?
A brand new micro fiber cloth fresh out of the bag is probably ok. But after that there is a chance of some hard dust particle from previous use or just from dust in the air imbedded in the fabric. It is far safer to use disposable tissue each sheet of which touches the lens only once.
It depends what's in the lens cleaner. Some glasses cleaners can have waxes or oils to fill the scratches in the eyeglasses. Or other unwanted contents. Best to use lens cleaner that's specific for photographic lenses.
I stlll use Kodak lens tissue and Kodak lens cleaner. Harder to come by these days but I have a fair supply. You can still get both off ebay. Sometimes under different labels.
I don't completely follow the standard directions but here goes, realize that watching me do it will tell you more than these words, my technique I learned from my father who was an excellent photographer:
Start with a blower and lens brush. Blow the lens off, blow the brush off. Then brush the lens lightly with the tip of the brush to dislodge particles. Combine that with more blowing. (If I don't have a blower along I'll use my own breath carefully but you have to be careful about the moisture)
Note the oils may streak with the brush and may contaminate the brush. If you are sure there are no particles on the lens you may want to avoid contaminating your brush and just brush with blowing with a bunched up lens tissue used like a brush.
I then get out a few sheets of lens tissue ready to go. Then I apply one drop of the lens cleaner carefully dead center on the lens being very careful it does not flow to the side. (most instructions say to put it on the tissue but I've always done it this way as it's easier to flow it on the lens. The issue is to avoid the cleaner getting into the lens mount and around the other side of the lens) This is mopped gently around the lens in a mostly circular motion without rubbing with a slightly bunched sheet of lens tissue. (you are trying to pick up any particles doing this) Follow with a new clean piece of lens tissue to clean and polish the lens very lightly while removing the last of the lens cleaner. (this may actually turn out to be more than two tissues used) Use absolute minimum pressure at all times. Do not use the tissue much after the lens surface is dry. Blow off any remaining lens tissue fibers. Then examine the lens carefully.
Any streaks on the lens surface repeat the mop and clean with new lens tissue. Pay attention all the way out to the edge of the lens. Scrubbing or rubbing with any pressure to speak of is to be avoided. A lens as oily looking as yours will probably take more than one round.
Once the lens is perfectly clean then put the perfectly cleaned filter on and leave it on. For most lenses even polarizers can be screwed onto the filter if they are used. You will have to use your own judgement here. But effectively you want that filter outside surface to be all you need to clean. Use a quality multicoated filter for this protective filter and always use your lens hood to keep down excess light hitting it. And use a lens cap when not using the lens.
When you are done you will have a little pile of lens tissue to throw away, don't reuse it, at least not for cleaning lenses. Make sure and protect your supply of lens tissue from dust. The original Kodak tissue came in packaging that did a lot toward doing that with a folder inside an envelope. I keep those in a ziplock in as clean a part of my camera bag as possible.
That's more or less it. Just remember no matter how careful you are each time you do this microscopic amounts of the coating get worn off. So clean sparingly and protect the cleaned lens surface. On average I have to clean my lenses less than once a year, the protective filter outer surface has to be cleaned more often. But if it's coating is damaged it's cheaper to replace.
I always give any used lens I'm thinking about buying the third degree about their surfaces. That's particularily necessary if it's a lens that did not have a protective filter or was otherwise cleaned lots. The wear of the coating is the why of protective filters, not the blows breaking the lens, which is extremely rare if you are careful.
Note the back element of the lens can also need cleaning. and that can be quite a problem on some lenses though the technique is basically the same. Use a back lens cap always. And a blower is all you will need most of the time.
Walt