Go to the Avast! website and Register your details (also make sure you check the box that it is for private use).
You will be sent an e-mail with a long term registration number - open the Avast! panel, open the menu from the top left link>About and then delete the demo number before instering the new one you have been sent (cut and paste is easiest way).
Whilst you are on the Avast! website you might as well download the latest version (if you haven't already got it).