It takes time and lots of patience. That's why it's worth doing.
Fish get sick because of a combination of two things; environmental stress that crashes the fishes immune system, which is their slime coating and the existence of parasites. Obviously, in the ocean they are constantly exposed, but their slime coat protects them. Tangs have very thin slime coats, so stress will get them exposed first.
So it's the basics that matter, water quality and a low stress environment. Good feeding habits also decrease stress.
As to corals, again it's water quality along with flow and lighting.