The email you receive (containing the serial number) includes detailed instructions on where to enter it. You must have an internet connection to activate. Be sure to copy/paste the serial number rather than trying to type it in.

Where to enter the serial number:
ON WINDOWS:
-Go to your Windows START menu (bottom-left corner of your screen), click and choose 'All Programs' -> 'Dream Aquarium' -> 'Enter Serial Number'
-Paste the serial number into the box and it will upgrade you to the full version.

ON MAC:
-Open your Screensaver Preferences (System Preferences->Desktop & Screen Saver) and click the 'Options/Settings' button.
-Paste your serial number into the field provided and press ENTER.