World of Warcraft Dragonflight takes you to the Dragon Isles for the first time, and of course you can also visit a new capital city.
How do you get to the capital from The Waking Shores in Dragonflight?
To get there, you'll need to complete a series of quests that begin in your faction's capital city: Stormwind for Alliance and Orgrimmar for Horde. The quest that takes you to the new zone is called The Dragon Isles Await.
Opening your map and quest log is the best way to track your progress towards that quest chain. In the upper right corner of that page, you'll see information about the Dragonscale Expedition campaign.
On the Horde side, you’ll grab The Dragon Isles Await from an NPC named Naleidea Rivergleam. The Alliance will get their quest from Toddy Whiskers. The quests will see you take a zeppelin or boat respectively, which will take you to The Waking Shores.