The Suramar Teleporter or portals are connected to Shal’anar, your main base. The first quest to unlock the portals is Oculeth’s Workshop. Once you finish Oculeth’s quests he comes with you to Shal’aran where he becomes your Chief Telemancer. The only portal I think requires a quest from Shal’aran is Falanaar. All other teleporters, you have to physically encounter them, and the teleporter pad itself has a yellow exclamation sign to start a quest. You must have 100 Ancient Mana to complete the quest and to activate that portal.
For now, ignore Falanaar if you don’t have it, you will eventually unlock it with the quest that sends you there; and focus on hunting down the other teleporters. The only teleporter that is hidden from view is The Magisterium, which is deep beneath Suramar City. You can find the entrance by the Terrace of Order near the Parade Grounds. It’s the tunnel that leads to the Suramar City The Arcway dungeon. The teleporter and its quest can be found in the area where you see Nightborne prisoners.
The teleporter to Falanar is unlocked with the quest “Cloaked in Moonlight” — given by First Arcanist Thalyssra in Shal’aran. You might need to feed her 100 Ancient Mana before she gives the quest.
Check out the map below. (Special thanks to Erixi for suggesting the missing one: “Aethenar”)