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 contact me on Twitter @PrestonDvorak.
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.
December 2, 2016 - Updated Mastery information to indicate there is no longer a cap on the number of HoTs that can contribute.
November 4, 2016 - Updated enchants to reflect Mark of the Claw proc'ing from heals again. This is now the top enchant for large-group healing.
October 29, 2016 - Updated stat weights based on my new simulations and information in the community. This didn't change much as far as BiS lists.
October 25, 2016 - Updated the guide for 7.1, including small talent/spell tweaks and an update to the Best in Slot list to include Karazhan loot.
October 15, 2016 - Updated stat weights, added Best in Slot list, and expanded the Picking Trinkets section.
October 13, 2016 - Updated some spells and talents with new usage information after having a chance to use them at max level in raid and mythic dungeon situations.
September 19, 2016 - Added actual stat weights to the "Stats and Gearing" page. Also added alternate weights for small-group content.