Unlimited API access is currently available as an add-on for users with a Pro level subscription. If you would like this feature, contact support.
In order to take advantage of the Disqus API, you'll first need to register an API application here.
After registering you'll be provided with a Public and Secret API key here.
You'll need these keys if you're looking to pull JSON data through the API or setup Single Sign-On (SSO) authentication.