We suggest you start by reading the Installation Guide, which covers downloading the code, and unpacking, configuring, building and installing. It then shows how to build the example programs.
For a quick introduction to our software, including a walk-through example of an application for searching through some data, read the Quickstart document.
The Overview explains the API which Xapian provides to programmers. A full API Reference is automatically collated using doxygen from documentation comments in the source code. There's also a list of deprecated features which lists features scheduled for removal, and also features already removed, along with suggestions for replacements.
If you want to learn more about probabilistic information retrieval, there's a (reasonably mathematical) introduction to the ideas behind Xapian which also suggests some books you might want to read.
For those wishing to do development work on the Xapian library itself, there is documentation of Xapian's internals available.
We also have a wiki for documentation and examples contributed by the Xapian community.