Healing doesn't really have a rotation of spells to go through like a DPS spec does, however, there are often certain types of situations that arise where you can respond in a certain fashion. I've detailed some of the most common situations below, as well as how to heal them. In the heat of battle, you may not always be able to stick to these things exactly, but with a little practice they should become second nature.
If you have any quetions or feedback, you can leave a comment below or tweet @Daemagor.
June 15, 2017 - -Reworded AoE tips, tier, and talents.
June 11, 2017 - Reviewed guide for patch 7.2.5. Updated BiS lists, stat weights, legendary items, and talent builds.
April 27, 2017 - Drape of Shame spreadsheet.
April 20, 2017 - Added the addons page with WeakAura information.
April 2, 2017 - Added Tomb of Sargeras gear and new trinket simulations to the stats and gearing page; updated the empowered artifact traits paths.
March 28. 2017 - Added Pawn Import Codes for stat weights.
March 27, 2017 - Tweaked "Top legendaries" lists.
March 27, 2017 - Reviewed and updated the guide for patch 7.2, including talent and legendary changes, and empowered artifact paths.
February 25, 2017 - Updated BiS gear list with minor changes to waist, boots, and chest, along with adding legendary items to the list itself, and major updates to the trinket section.
January 20, 2017 - Fixed "Breakdown by Boss" counts for BiS list.