There are numerous guides on how to complete each of the main encounters in the King's Fall raid in Destiny: The Taken King, the game's final challenge. Despite being well written, none of them are anywhere as good as teaching players how to complete the raid than actually being in the raid and having someone who knows what they are doing to walk the fireteam through the entire process.
Even watching video tutorials doesn't really help, as they do not offer the viewer a proper vantage point of the action, which is often obscured by distance, enemies, and obstructions.
To that end, a redditor named EightBitNacho has developed a solution by offering a series of GIF guides to each of the main encounters in King's Fall, except for the maze and the two platforming sections in the middle, which have quite a bit of verticality and require trial and error.
In each GIF guide, EightBitNacho explains the basics of the mechanics and strategies that his fireteam uses to complete King's Fall.
Annihilator Totems
Warpriest
Golgoroth
The Deathsingers
Oryx
Keep in mind that there are some slightly different strategies floating around for the Golgoroth fight, which may involve shooting down all six orbs. Furthermore, the guide is only applicable to the normal difficulty version of King's Fall, and more advanced strategies may be required for the Hard mode version.
Be sure to check out our guides on the fastest way to earn Legendary Marks, Infusing weapons and armor, the fastest way to raise your light level, and how the Exotic Blueprint system works. Here's our guide on finding all 50 Calcified Fragments.