There are several suggestions for you. First of all, you should choose the specific cleaner that is made for photochromic sunglasses or can be used for most sunglasses. Secondly, you should use a piece of soft cloth to clean your sunglasses instead of using your fingers. Because there are a lot of bacteria and dirts on your hands. At last, you'd better develop a habit of cleaning your sunglasses very often.
It is the same as you clean other sunglasses lenses. First of all, you shall wet your transition lenses with water. Then, rub both sides of the left and right lenses with optical lens cloth. Next, Use a drops pf mild dish soap in warm water and wash your prescription photochromic sunglasses with the water. Then, use clean water clean your lenses. At last, dry glasses photochromic lenses.
It is similar to the way to clean other glasses. At first, wet you sunglasses' lenses with water to avoid scratches. Then, rub the lenses with a piece of optical lens cloth to remove the dirt. What's more, drip a drop of soap-suds into a bowl and put 2 cups of warm water for blending with the soap-suds. Moreover, put your sunglasses into the soapy water, then rush them with tap water. At last, try the sunglasses again with the optical cloth. You should make sure that never use window cleaner to clean your transitions lenses, which is very harmful for your photochromic sunglasses.