Bungie is making it much easier to earn Faction Reputation for Dead Orbit, Future War Cult, and New Monarchy when The Taken King (opens in new tab) arrives. In Destiny's first year, players needed to wear a respective class item in order to earn Faction Reputation. These Titan Marks, Warlock Bonds, and Hunter Cloaks are still available to purchase at the Faction vendors, but now you are no longer tied to wearing the colors of your chosen faction, you only need to swear allegiance to them.
Swearing your fealty doesn’t require a grand deed or blood bond, just a quick conversation and some cash. Head to the Tower and speak to the faction leader of your choice. New Monarchy's faction vendor, Executor Hideo can be found near the Speaker, down the corridor to the left as you enter the Tower. Arach Jalaal is Dead Orbit's faction vendor and can be found down the right corridor, on the left, and down the set of stairs. Finally, Lakshmi-2, Future War Cult's vendor is up the stairs from the Shipwright.
Once you speak to the faction vendor, they will prompt you to Accept Allegiance with them for a small fee of 2,500 Glimmer. From that point, the Vanguard and Crucible reputation points you earn will go towards your chosen faction reputation.