You can also use materials to level your faction. Each faction will allow armor, weapon parts, or certain planetary materials, special or heavy synthesis to be turned in to gain more rep. Rep boosters help too like in CoE with Variks. Patrol Bounties help as well since some planetary patrols are tied to certain factions. Hope that helps

If you have your alliance with the faction then basically you just play the game. Faction rank goes a bit slower than vanguard and crucible rank but if you just do a lot of things you'll get a lot of rank.