I am quite new to Java, and need to work on a project requiring using open source software. I am very confusing about understanding those Java API's documentation.
Please refer to the following link, and show me how to use the related java class, RemoteXmlSimpleSearchEngineBase, based on its Java API.
You won't be using it directly, because this is an abstract base class.
A base class for implementing data sources based on XML/XSLT.
If you are actually looking for a concrete usable implementation you should have a look at one of the listed known subclasses, which are EToolsDocumentSource, GoogleDesktopDocumentSource, and SolrDocumentSource.
If you plan to extend it read the API contracts carefully and maybe have a look at the source code of the concrete subclasses for hints on how to proceed.
Build a man a fire, and he'll be warm for a day. Set a man on fire, and he'll be warm for the rest of his life.
Just to add a little more to what Jelle said, API docs can be pretty indecipherable when you look at them without any context. I would start by reading through the Carrot2 documentation on this page. Once you have an overview of what the package can do and have examined some code examples, then the specific classes and methods in the API docs should make a lot more sense.