I have previously purchased a download of CS6 Design and Web Premium. I want to install it on my new laptop but I'm not sure how. I still have my product code/serial number from my purchase back in December 8, 2012. What can I do to transfer my softw

Just install and activate it.  If you need to download the installation files you can do so thru the link below.

Your license allows you to have two activated installations, so if you only currently have the one, you can still install on another machine without touching the original installation.  If you prefer not to retain the original installation then you should deactivate it as a minimum by opening one of the applications and choosing Help -> Deactivate.

CS6 - http://helpx.adobe.com/x-productkb/policy-pricing/cs6-product-downloads.html

You can also download the trial version of the software thru the page linked below and then use your current serial number to activate it.

Be sure to follow the steps outlined in the Note: Very Important Instructions section on the download pages at this site and have cookies enabled in your browser or else the download will not work properly.

CS6: http://prodesigntools.com/adobe-cs6-direct-download-links.html