Your library account and your Mango Languages profile are different. If it's your first time using Mango through your library, you'll need to create a Mango profile. Again, this is different than your library profile, which you may log in to using your barcode, library card number, and/or pin.
To get started, click on the Mango Languages link on your library's website. There you can create a Mango Languages profile, if you don't have one already.