Unit test ( as already mentioned) and build up static json/xml/whatever files to run your code against so that you can integration test your stuff without integration testing the 3rd party stuff.
At some point you end up outside of the scope of testing, but you can build bootstraps to make sure that your mocks match whatever they are mocking.
Obviously, this does you no good when something like an API service goes down, but that's issue is irrelevant to the question that was posed. Having some static file to test against whether it is accurate or not will instantly tell you whether it is your code or the third party that is breaking.
