After deciding to fight with Nohr, you must battle the Hoshidans.
Rout the Enemy
Move your party up toward the Dragon Vein, then use it so you can reach Xander and help him fight Ryoma. After you heal Xander and get rid of Ryoma, attack the other Hoshidans one by one until they are all defeated.
After the battle, Lilith takes you to your castle in the astral plane and walks you through creating buildings. At this point you can have Support conversations with your units, invite an ally to your private quarters (be sure to select someone with a heart icon next to the name because this will ensure that your relationship will improve), collect resources, and buy stuff from the shops.
Be sure to feed Lilith. You might want to check on the crystal ball to visit other castles (if you are connected to the Internet) because this will let you gather resources that are unavailable in your own castle, giving you a wider range foods to give stat boosts to Lilith.
When you are ready, press Start to go to the castle menu, then choose Next Battle. There will be several options. The Dragon's Gate lets you purchase DLC (be sure to check for free DLC). You can also change the difficulty here, and side battles will be listed here as well.
To continue, choose the Chapter 7 option from the castle menu. The game will progress to Chapter 7: A Dragon's Decree.