Vanguard Marks are the high-end currency for better gear in Destiny. The Vanguard Quartermaster sells certain loot for Vanguard Marks instead of Glimmer.
Before you can begin earning Vanguard Marks, you have to be a minimum of level 18, however I suggest waiting to farm them until at least level 20 since the level 18 strike playlist does not reward marks.
Marks are earned primarily by completing strikes, bounties, daily heroics, and weekly heroics.
You won’t have access to the daily or weekly heroics until level 20, so from level 18 to 20 you’ll only be able to earn marks through strikes and bounties.
Surely you know all about strikes by now, so I don’t really need to explain those. Higher level strikes obviously award more marks per match, if you can beat them efficiently.
Bounties can be received from Xander 99-40 in the Tower. Bounties will be things like “Kill 10 Fallen Majors or Ultras” or “Collect 200 Olympus Tears on Mars”, etc. These are repeatable, and you can have five bounties at once.
Vanguard Marks can also be attained somewhat randomly from the Quartermasters in exchange for raw materials. There is also a chance of receiving rep when trading materials, so it’s not 100% efficient, however it is a nice way to supplement more marks.