Sphinx4 API is provided by a single jar - sphinx4/lib/sphinx4.jar. You only need to include this jar into classpath or into the project in IDE and use the API. Sometimes you need to include other jars from sphinx4/lib folder.
For tutorial on using sphinx4 see
http://cmusphinx.sourceforge.net/wiki/tutorial
it has sphinx4 section which will help you to start with the API. Also see the code of sphinx4 demos.
To get idea how to include jar into the IDE project, study IDE documentation. Here is the howto for Eclipse: