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 exaplains the API which Xapian provides to programmers.
Much useful documentation is automatically extracted from the source code. Full documentation of the API is available for users. For those wishing to do development work on the Xapian library itself, documentation of the internals is available, and there's a short document outlining the directory structure which is automatically generated from the source code.
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.