Hotest water you can stand. Blast copious amount over lenses, both sides. This removes some grease and large grit. Put several drops of detergent on finger tip and rub onto thumb tip. Using thumb and finger coat detergent onto both sides of both lenses then rub gently. A few seconds is all you need. This removes all remaining oils and suspends any remaining grit preventing friction scratches during cleaning. Rinse lenses with hot water and gently dry with paper towel. Hold up to light to check progress. Remaining smears if any come off with paper towel. Been doing it for decades. It never scratches and it cleans like new.
This is really bad advice, about hot water. When I was in New Zealand once, where you sometimes still encounter faucets with a separate hot water and cold water tap, I accidentally ran my glasses through the very hot water coming out of the hot water tap and it completely destroyed the coating on the lenses, it was as if I had run sandpaper over them.
The water only needs to be lukewarm. i.e. rinse glasses with lukewarm water, then get a drop of dish soap on fingers and rub fingers through a bit more water to dilute the soap, then gently scrub the lenses as you describe, and then rinse the glasses again with lukewarm water. Almost all the water will sheet off.
I would strongly advise against paper towels. With bad luck these contain small splinters of wood that might be just as sturdy enough to cause small scratches. Happened to me on a pair that I had just worn for 6 weeks.
