On the IBM developerWorks site, there's a tutorial from Vikram Vaswani showing you how to connect to Wikipedia's API in your PHP application. It shows how to fetch, search and update entries through their backend. The tutorial's a little bit older (from May 2011) but the content is still relevant.

Wikipedia is the ultimate online encyclopedia, containing millions of entries on different aspects of human knowledge. Web application developers are able to access and search these entries through the Wikipedia API. This article introduces the Wikipedia API and demonstrates it in the context of a PHP application, explaining how to search and retrieve different elements of Wikipedia content with PHP.

He starts with a general introduction to the API including example feed results and URL request formats. From there he moves into the code - a mostly Zend Framework-driven example that uses the REST client. He shows how to make requests for categories, full-text search, grabbing raw page content and adding/editing the content of pages.