Launch the Checkout application on your computer (if you don't have it yet, you can get it by clicking 'Agree' on our download page over here. After Checkout has opened and you have agreed to the License Agreement (that's only shown the first time you launch Checkout) a Welcome screen opens.
The menubar on the top of your screen will have a 'Checkout' menu right next to the Apple menu. Select that menu and click 'Registration...' there, that should open the registration screen.
After filling out the form, entering your serial number in the 'License Code' field and clicking the checkbox next to 'I Agree to the License Agreement', click the 'Submit' button at the bottom of the window. Checkout should now show you a screen that say it's been registered to your name. After you close that screen, you can start using Checkout.