If you are no longer using the old computer, you should sign out of the program via the Help menu.
You should install the program from scratch on the new computer. This link will take you to the Products page of your Adobe.com account. There you will find download links for your registered products and the serial numbers for each.
If you use the Organizer, you need to backup your Catalog(s) from the old computer and restore them to the new computer. See this article for more details.