You are asking some general questions here. Nothing wrong with that, but healing is variable-based way moreso than the other two sides of the trinity, so instead of telling you "do this and that in X encounter's Y -phase", you should be mechanically aware as a player and understand how skills work - tank cooldowns and their icons, paying attention to your healing partner and trying to synergize, paying attention to the amount of incoming damage roughly and acting accordingly. Things like that.

I would say that being able to sort of have a feel for the incoming damage and the internal timers of a given fight is paramount, as this allows you to mindmap the encounter, plan for precasting, buffer tanks when need be, cruisecontrol and multitask when possible - stuff like that. To get to that point, you need to: 1) have at least some experience in the fight. 2) be of the type who analyzes fights in full in one's head.

Beyond that, if you understand this game's aggro mechanics, pay attention to what tanks do (their cooldown icons, etc.) and try to synergize with your healer partner and sharing responsibilities - it's mostly just finetuning. Not sure how I would give you "numbers" or any encounter-specific tips, unless you have some specific questions in mind.