Before you book a tour, ask the dive/snorkel operator whether he anchors on the reef. If he does, go somewhere else;
If you don’t feel comfortable in the water, consider not going (or look for a glass bottom boat!). Uncomfortable in the water means a lot of fin movements on the wrong spots;
Practice your diving in a pool until you have 100% buoyancy control before going out on the reefs. A lot of coral breakage is done by divers that can’t control their buoyancy well and that is not something you should learn diving on a fragile reef;
Never touch corals, even if they look dead;
Dive with your head down and fins up in order to not touch coral with your fins or gear dragging over the sea floor;
Stay on a safe distance from the reef, especially with currents your height is varying;
Don’t bring a camera on your first 20 dives. To work with equipment underwater requires some skills and perfect buoyancy. Any distraction underwater can lead to rampage and divers crashing on corals;
Still eat fish? Well, think about it twice to order that fish you saw on the reef. Did you see it in abundant numbers?