How do I clean an evaporator coil?

Very carefully with a brush. If this is under your refrig, then use a long handled brush that you can buy at a hardware store or at Walmart for about $4. If this is for your a/c then you can use an old soft toothbrush taking care not to bend any of the fins.

If it is a/c units I always used a soft birstle bruch with bio degradable degreaser. I concur with twinkiedooter!