I need to move my copy of CS6 from my old computer to a new one. Do I need my license reset?

You are allowed to have the software installed and activated on two machines, so there is nothing you need to do other than install (not move) the software on the new machine, unless you already have it activated on two machines. 

If you do not plan to use the old machine again or would simply prefer to remove the software from it, or you would like to retain an activation for another machine at some point, it is best that you deactivate it beforehand.  To deactivate open one of the applications and choose Help -> Deactivate.  Once you deactivate it there is nothing else you need to do unless you want to uninstall it as well to gain more drive space.