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 questions or feedback, you can leave a comment below or contact me on Twitter @PrestonDvorak.
March 23, 2017 - Reviewed and updated guide for 7.2, including new artifact traits and minor talent updates.
March 20, 2017 - Added initial addons page with Grid and WeakAuras overviews.
March 17, 2017 - Updated legendary item list with simulation data.
February 21, 2017 - Did a full review and update of all trinket ranking information.
February 12, 2017 - Added Perfectly Preserved Cake to BiS trinket list, below Etraeus' trinket and the legendary trinket.
January 25, 2017 - Updated small-group stat weights and BiS list.
January 18, 2017 - Added Pawn Import strings for stat weights.
January 17, 2017 - Moved the Macros guide to its own section. Overhauled the Stats and Gearing page for 7.1.5.
January 12, 2017 - Overhauled legendary information and added best in slot legendaries to both BiS lists.
January 10, 2017 - Updated guide for 7.1.5, including adding Nighthold items to Best in Slot lists.