It's not too hard, the tough thing is keeping in mind that you cannot let anything that your fingers or skin has come in contact with touch the glass. I use a pair of tweezers to put on a surgical glove (the kind without powder), use tweezers to put the first glove on one hand, then the glove hand can put the glove on the bare hand. Those tweezers can't be touched by a gloved hand! Also, every tool, can of air, everything must be cleaned first, so that no oil from skin that may be on the tool will get onto the glove then find it's way onto the cleaning cloth, then onto the glass.
Remember that internal coatings can be softer than the external coating. I use a microfiber cloth sold in eyeglass cleaning kits.
I also use the cleaning fluid in the eyeglass kit, misted onto the cloth, then use distilled water to clean the little bit of fluid off the glass. Be gentle!
When fitting the clean and dry element back in, I use a can of air as sold to clean computer keyboards. Blast the dust from inside of the lens assy, then keep blasting air some while the element is lowered into place.
Dust and most of all skin oil are your enemies.
The way NOT to clean lens elements is with paper lens tissue, bare hands and worst of all, wiping a few wipes then-horror- turning the tissue over so the oily part that was in contact with fingertips gets smeared onto the glass..
Just remember, nothing that has been touched by fingers, and nothing that has been touched by something that has been touched by fingers can be used to wipe the glass.