How do I log into my account from a new phone?

Make sure you have bound your game on the old device to an external account. IM30, facebook, google play etc.

Go to Settings > Account > Bind Account

You can then load the game on any other device, and after completing a bit of the tutorial you can access the settings and log in with the same external account to recover the progress.

Go to Settings > Account > Switch Account to log in.