Registering: Press the EVE Online App button and log in with your main character. The program system will create you a new user that you can then use to log in.

You will be not logged in after your registration and you will have to log in again after successfully registering a new character!

Log in: If you have already created an user as described above you can simply log in by using the same character you created your account with by using the same EVE Online App button.