As you progress through the story you will unite the 3 Vanguard members (Zavala, Cayde-6, and Ikora) and they will join all the other vendors at the Farm and will be told to speak to them.
Upon speaking to Cayde-6 you will be tasked with completing a milestone in the EDZ (Earth) to place down patrol beacons. Once the patrol beacons have been placed, you will be tasked with completing 3 patrols (just like in Destiny).
Once you've completed 3 patrols, return to Cayde-6 and you will unlock the milestone for completing public events in the EDZ. After completing 6 of these you'll be told to go speak with Cayde-6. After speaking with him the achievement will pop.