There is not a easy way to clean an evaporator coil that I know of. When I was servicing furnaces (clean and check). I would always take the blower out of the furnace, clean the blower wheel and blower motor. While I had the blower out I would look up through the heat exchanger with a flash light to see if the evaporator really needed cleaning. This requires that you slide into the furnace blower compartment on your back and shine a flashlight up so you can see if the bottom of the evaporator is dirty or not. I did not want to go through the trouble of taking the sheet metal off from around the evaporator and find that it was not dirty and that I had wasted my time so while I had the blower out it was easy to inspect the bottom of the evaporator coil. If the evaporator coil was dirty and while the blower was out I would use a spray coil cleaner, a fin comb and a vacuum cleaner to clean the coil. It is quiet time consuming, but I was motivated by knowing that if the coil was dirty and stopped up, then the customer would notice a big difference in their heating and cooling air flow and their heating and cooling bill.