After installing Articulate Studio '13, you'll have a 30-day free trial that doesn't require activation. Studio is fully functional during the trial period.
When the trial expires, you'll need to activate Studio with a valid serial number to continue using it. You may also activate at any time during your trial. If you don't already have a serial number and you'd like to purchase one, click here.
One serial number for Studio activates all the products purchased with your license. You won't have to activate each product separately. Just activate any one of the products you purchased, and the others will activate at the same time. See these articles for activation instructions: