The APIs are web service APIs which can be accessed from many different languages. This web site includes examples of API usage in several languages, including PHP and the Support forums include more examples.
For PHP, you might consider starting with this example, which is focused on Authentication:
http://developer.constantcontact.com/OAuth/SamplePHP (shows OAuth Authentication)
or with this example, (which uses Digest Authentication):
http://developer.constantcontact.com/doc/samples
Or, take a look through the forums for more examples.
Thanks,
Tom M
Group Product Manager – Content Editing
Constant Contact