Getting Started with Xapian is the recommended place to start, and contains updated versions of many of the documentation pages which used to be here.
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 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.
The deprecated features section of the "Getting Started" guide lists features scheduled for removal and 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:
The Xapian Developer Guide contains information for those wishing to do development work on the Xapian library itself.
We also have a wiki for documentation and examples contributed by the Xapian community.