I've not had to use these yet, so when I hit Kupo Mission 9 (Rescue! A Moogle's Labor of Love) and the various guides I looked at referenced Green Map Markers, I had no idea what they were talking about.
I've only been playing this game a couple of months and sometimes I feel like guides on various sites are written with the assumption that players just know where things can be found in this monstrous game.
If you're on a mission where an NPC is adding Green Map Markers to your map, you can view those map markers here.
On the map screen, find and click the markers button.
It will open the user (purple) customizable markers.
Hit the left or right keys on your keyboard and the list of green quest markers will appear.
Note, for active markers, you must have a map open where active markers exist. For example, there are 8 maps in the Qucksand Caves and the ??? you need to find can be randomly distributed among those 8 locations in the Kupo 9 mission.