You log on via the route that you used to sign up, either via a username and password, Facebook or twitter. Just enter your details or hit the buttons and you will be signed in.
You do need an internet connection for this part. The app does not work by magic. Yet ;)
If you forget your username or password then just hit the Forgot password button and this will ask you to fill in your email address. You will receive an email with a reminder of your username and instructions on how to reset your password.
Happy logging :)