The Factions Leaders as well as the (almost) full functionality of Destiny Factions is now live on the server. Visting the faction leaders, Arach Jalaal, Executor Hideo or Lakshmi-2, will let you join the faction you wish to align yourself with.
You can donate materials to the leaders to gain reputation, which you can view with /faction. The rates are exactly the same as in Destiny, so the grind is truly real. After leveling up, you'll get a Faction package which is decodable like a normal engram is. There's a 2 hour cooldown between faction changes, so it's much more lenient than the 1 week that actual Destiny has. Bear in mind that they're asking for Ammo Syntheses, not normal ammunition. You can buy Ammo Synths from the Gunsmith.
There are 3 "ranks" to the Faction, but since I'm too lazy to implement them you can just buy whatever you want from them with Legendary Marks.