So you’ve got a bunch of Vanguard Marks in Destiny, but you can’t do much with them without gaining ranks in the Vanguard, which requires certain amounts of Vanguard Reputation.
Legendary armor requires Vanguard Rank 2, and legendary weapons require Vanguard Rank 3. Here is the breakdown of how much reputation you need for each rank:
Vanguard Rank 1: 1500 rep
Vanguard Rank 2: 2000 rep
Vanguard Rank 3: 2500 rep
There are further ranks as well, which will grant you some free legendary equipment for each rank, and a Vanguard Commendation which you will need for some of the bigger purchases as well.
The best way to gain Vanguard Rep is by completing the Vanguard bounties. It’s extremely important to run these bounties every chance you get, as they typically give you the best rep for the least amount of time. Some bounties are much better than others however, and some bounties I don’t even mess with because they simply take too long, like the “Get 20 double kills with a Fusion Rifle” bounty (that’s not the exact bounty name obviously, I can’t remember what it’s called at this time) which seems nearly impossible even on lower level enemies.
The next best way to farm Vanguard Rep is by completing patrols. Patrols give considerably less rep compared to bounties, but if you have completed all of the Vanguard Bounties for the current lockout time, you don’t have much of a choice.
If you have a couple friends to farm Patrols with, I found a guide for farming Vanguard Rep that looks intriguing.
It basically requires you and two friends in the Cosmodrome on Earth to spread out and cover three different areas of the map for maximum coverage and fast Patrol completion. You can gain several hundred rep per hour with this method, and the video claims you can gain up to 800 rep per hour if you get really efficient at it.