Interface
As a healer make sure you take care of your UI. Set up whatever raid frames you are using to clearly show all the information you need such as debuffs, personal defensive abilities, external defensive abilities and absorbs.
Here is my UI in combat:
Macros
Mouseover Healing Macros
Unless you are using an addon like Clique I suggest using Mouseover Healing macros such as this:
#showtooltip
/cast [@mouseover] Healing Wave
You can do this for all your targeted healing spells.
Cursor Healing Macros
You can make your Ankh Totem, Spirit Link totem and similar abilities instantly cast on cursor position without needing to click. This can help you save a life faster:
#showtooltip
/cast [@cursor] Ancestral Protection Totem
Weakauras
Cloudburst Weakaura similar to the one I use: https://wago.io/SJwu0_2EW
High Tide Weak aura similar to the one I use: https://wago.io/rk7idBBoX