There's a new Getting Started with Xapian guide, which is the recommended place to start.
The Omega search application has its own documentation, and there's also separate documentation for the other language bindings.
We suggest you start by reading the Installation Guide, which covers downloading the code, and unpacking, configuring, building and installing it.
The glossary provides definitions for specialized terminology you might encounter while using Xapian.
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 information retrieval, there's a (reasonably mathematical) introduction to the ideas behind Xapian which also suggests some books you might want to read.
There are a number of documents which cover particular features:
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.