Discovering an API
Go to API Central and select "APIs" from the top menu bar. You'll be able to browse and search the APIs available there. Click on any particular API to see details and to try it out using the interactive docs.
Requesting Access to an API
Once you've set up an account on API Central, you can request access to any API by "adding credentials." Go to the API on API Central and click on "Add credentials for this API" then fill out the resulting form. If the API is restricted, we'll work with the data steward who controls access for that API and get back to you with his/er decision.
WORKING WITH an API
Once you've got access to the API, you're ready to build a client into your code base. For examples of how to do this in several popular languages, take a look at this handy blog post on MashApe. If you need help understanding RESTful APIs in general, there's a good brief tutorial available on-line called Learn REST.
Of course, you can also always ask for additional help at firstname.lastname@example.org.