If you have used “Sign in with Google” button to register the first time, you are welcome to continue using Google for future sign in also. Google does not send PADT website your password – so PADT in this case does not store any password for you.
I would recommend using this method as the best way to register and also to sign in to PADT.
If after you have registered using “Sign in with Google” button – and then later you want to sign in directly – you will have to click on the “Forgot your password” link at the bottom of the login form which will send you a mail (with a link) to create a password for PADT website. You can choose a password (which can be different from your Google password), and you can use it to sign in directly in PADT website with your username/email and new password. However you will continue to have the ability to sign in with Google whenever you want.