If you got a Beta key and don't know where to use it, go here to register. Once you've registered, you can login to the game here.
I got a mail from madmini that said: "Thanks for applying for the Card Hunter Beta. To activate your subscription, please follow the link below." I clicked the link, but accidentally closed the page before I filled out any account info. Now when I click the link I get "Already activated". How do I re-enable my code (or get a new one) so I can join the beta?
You don't need to - you activated your subscription to the newsletter it seems. Signing up or registrating for beta isn't an automatic beta key generator - so can take time before you recieve a separate mail with a beta key.