After the Eorzean Alliance leaders agree to hold a memorial service for those who fell at Carteneau, you are asked to meet with Baderon in Limsa Lominsa.
Optional: The Gold Saucer
Now that you have completed one of the three Envoy quests listed above, you can unlock the Gold Saucer, a casino where you can play minigames to win MGP, an in-game currency that you can exchange for unique items. The quest to unlock it is in Ul'dah. Read the Gold Saucer page for more information.
Beginning the Next Main Scenario Quest
If you started in Gridania or Limsa Lominsa, talk to Bartholomew in Ul'dah to start the next main scenario quest, "Call of the Sea". If you started in Ul'dah, talk to the Serpent Officer near the Conjurers' Guild in Gridania to start the quest.
Speak with Baderon
Go to Limsa Lominsa. If you have attuned to all of the aetherytes in Limsa Lominsa, you can use an aetheryte to go to the Airship Landing, then talk to the Lift Attendant to go to the Drowning Wench. If you haven't attuned to all the aetherytes there, it is recommended that you do so, but until then, go to the Limsa Lominsa Upper Decks, then go to the central area to find Baderon. Talk to him to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Baderon to accept the next quest: It's Probably Pirates.