To change your password while in game:
Go the main menu, click Account and then Change Password. Type your current password, and then choose a new password. Tap Update, and log in with your new password.
To change your password while logged out:
After opening the game, you may see a list of usernames previously used on your device. Make sure the correct one is selected, then tap Select.
Your avatar will be displayed, then you can tap on the Sign In button, logging in using your username/verified email and password.
If you need to change your password, tap on Forgot Username/Password at the bottom of the screen and enter your verified email address. You'll then receive an email with instructions on how to set your new password.