Activating a GOG key is really easy, simply follow these short steps:
First, login into your GOG account.
Now enter https://www.gog.com/redeem.
Type the code you've received and click the Continue button.
In the next window also click the Continue button. Then you'll take to the final step.
On the next page, click Pay for your order now.
That's it! Your game should be visible in your library.