Fill in your personal data at the registration form. At some casinos you will choose a username and password, others present this possiblity at a later stage.
After the registration you will usually get a confirmation link in your email inbox. This link is meant to verify that you are really the person who signed up, and not someone else using your name. When you click on the confirmation link you can immediately log in and play.
You will choose a method of payment and make your first deposit. Now you will receive your bonus, which at some casinos can go up to hundreds of euros!