For *HORDE ALTS* ONLY!
Assuming that you have completed all of the questlines on at least 1 other character:
To unlock world quests:
1) On your alt go to Zuldazar and complete the quest: Battle for Azeroth: Mission Statement
2) Accept the next quest: The Stormwind Extraction and talk to Nathanos in order to skip the scenario
3) You will end up back in Zuldazar. Accept and complete: Welcome to Zuldazar
4) Finally find Nathanos on the Horde ship and accept and complete: Uniting Zandalar
5) Ta da!
To unlock Nazjatar zone:
1) On your alt go to Zuldazar and accept and complete the quest: Send the Fleet
2) Follow the storyline and complete the following 11 quests to unlock the portal back to Zuldazar
3) Ta da!
To unlock Ny'alotha, the Waking City raid:
1) On your alt go to Nazjatar and accept the quest: Essential Empowerment from Magni
2) On your alt go to Zuldazar and accept and the quest: A Dying World from the Earthen Guardian
3) Take the portal to Silithus hand in the quest A Dying World and accept and complete the quest The Heart of Azeroth
4) Accept and complete the quest: Infusing the Heart from Magni
5) Leave the chamber and re-enter to complete quest: Essential Empowerment
6) Accept and complete MOTHER Knows Best
7) Accept and complete A Disturbance Beneath the Earth
8) Accept and complete Dominating the Indomitable
9) Accept and complete A Friendly Face
10) Accept and complete The Heart Forge
11) Accept and complete Harnessing the Power
12) Go back to Zuldazar and on the Horde ship at /way 58.54 62.63 there will be a letter with the quest Return of the Black Prince. Accept and complete it.
13) Accept and complete Where the Heart Is
14) Accept and complete Network Diagnostics
15) Ta da!
Note: Apparently everyone can access the raid when it is in Uldum (not confirmed by myself). But to access the raid when it is in pandaria you MUST complete the questline above.