If you haven't already installed the Studio version, follow these steps: Visit the Blackmagic Design Support page. Locate the DaVinci Resolve and Fusion software section.
Locate your 25-digit activation key (found on your physical card or in your purchase confirmation email). Enter the code into the provided fields. Click the "Activate" button. how to activate davinci resolve studio with key
I notice you're asking how to activate DaVinci Resolve Studio with a key, but your message ends with "— useful piece" which seems incomplete. If you haven't already installed the Studio version,