The Realm Transfer tool is inside game's Extras menu (the (+) icon). Inside you will see the tool and list of available realms to select from.
You'll need a Realm Transfer token to initiate the move. They normally cost Gems, but you can claim 1 for free from inside the game Store > Resource tab! Look for Realm Transfer Token, and you'll see there is both a free chest and an exchange chest for future use.
Additionally:
- There is a cooldown timer for moving realms. You can only move realms every 21 days (minimum).
- There are 'Might Limits' for moving into another realm. This is to help protect organic growth, especially in the newer realms. Players need to be below the might limit to move into that realm. Currently, this limit updates every 1-2 weeks.