There are many ways you could find the API and examples of its use. 1. You could search these forums 2. You could search using Google 3. You could search the Alfresco Wiki (http://wiki.alfresco.com/wiki/Main_Page) 4. You could search the online Alfresco Documentation (http://www.alfresco.com/resources/documentation) 5. You could install Alfresco and use a browser tools to see the REST APIs that are called when performing actions from within Share 6. You could install Alfresco and view the WebScript REST APIs (/share/page/index/uri/ & alfresco/service/index/uri/)
You'll find that the Alfresco Community members are very willing to help resolve any problems and answer any questions you have, but there is the general expectation that you should do a little bit of leg work first.