Important: DeActivate your current SolidWorks Serial Number first.
Go to Windows control panel --> Add/Remove programs or run setup again from the installation. Choose the change or the modify button not the remove button. When you get to the serial number page change the number and choose next. After you choose next you can close the dialog. Start up SolidWorks and your new serial number will be active. You will most likely need to Activate again but that should be all as long as your Serial Number is good.