Building your faction reputation in Destiny: The Taken King is one of the slower activities you can participate in. Compared to earning reputation for the Vanguard and Crucible, earning a rep with one of the game's three factions will progress at a much slower rate, but the rewards you receive for doing so are well worth it.
There are three main factions in the game: Future War Cult, Dead Orbit, and New Monarchy. Each faction has their own unique armor and weapons that you can either purchase with Legendary Marks as you unlock ranks, or acquire in packages each time you rank up.
In Year One of Destiny, faction rep was built by equipping your class armor while completing quests. This has since changed. You must now pledge your allegiance to a faction. Once you pledge, you'll earn both Faction and Crucible/Vanguard reputation at the same time.
Besides doing quests for reputation, the new system also allows you to trade materials in exchange for reputation.
Motes of Light - 100 reputation per 5 (125 per rank)
Armor Parts - 50 reputation per 25 (1250 per rank)
Weapon Parts - 50 reputation per 25 (1250 per rank)
Special Ammo Synthesis - 25 reputation per 4 (400 per rank)
Heavy Ammo Synthesis - 25 reputation per 1 (100 per rank)
If you do the math, you'll find that the cheapest and fastest way to rank up your faction is by trading in Motes of Light, which drop like candy in The Taken King, and Heavy Ammo Synthesis.
You can buy Heavy Ammo Synthesis at the Gunsmith for 950 Glimmer each. Glimmer comes easy, so return to the Tower whenever you have close to 25,000 Glimmer in your wallet and spend it all on Heavy Ammo Synthesis. Then turn those in with your faction representative.
If you have an excess of Strange Coins, you can also spend those on Heavy Ammo Synthesis whenever Xûr's around. You can trade 1 Strange Coin for 3 Heavy Ammo Synthesis.
Beyond earning random Legendary items each time you rank up, you'll also get an Exotic faction quest once you hit rank 25, which rewards you with an Exotic class item such as a Hunter Cloak, Titan Mark, or Warlock Bond.
Here's what you'll need to do for the quests "For Future War Cult!", "For New Monarchy!" and "For Dead Orbit!"
While in the Crucible, you'll need to wear a shader, an emblem, and a piece of class armor from your faction of choice. Then complete the following objectives:
Here are some of the faction rewards you'll get for ranking up.
Future War Cult (The Taken King)
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. You can also find our guide on locating every Calcified Fragment in the game.