How do I teleport back to my state after alliance duel?

You can teleport home by finding a location in your home state and using the teleport option. If you are not sure how to do this go to the world map and tap the co-ordinates listed at the bottom to bring up an input. Change the state number to your own and then tap 'Go To'

Once on your home state map select where you want to port to.

You should be able to teleport home for free after alliance duel, if not you will need an advanced teleport.