Visit the WebApp and click the Facebook icon. This will connect Wunderlist to your Facebook account. Wunderlist will now operate using the primary email address of your Facebook account.
When you use this function, a random password will be generated. You do not need to see this password - we take care of everything in the background. However, If you wish to login using other devices using your Facebook credentials the 'not seeing the random password' decision will become a problem. In this case, you need to use the 'Forgotten Password' function to request a new password, one you can actually see! Use this with your Facebook email address and you're in! After that you can change the password to something more personal.