On your home screen click the menu button and then settings, Click on accounts. If Facebook is listed, make sure your e-mail and password are correct. If it is not there, click add account, choose Facebook, and enter your information. This will link Facebook to your messaging account and will bring in your Facebook inbox.
This will not give you alerts for people posting on your wall, commenting on status, etc. For that, make sure your Facebook account is setup to send you e-mail alerts for whatever you want to be notified of, and then make sure you have that e-mail linked to your phone using the same process described above.