You need Python 2.3 or later.
You need libxml2 and libxslt, in particular:
libxml 2.6.21 or later. It can be found here: http://xmlsoft.org/downloads.html
If you want to use XPath, do not use libxml2 2.6.27. We recommend libxml2 2.6.28 or later.
libxslt 1.1.15 or later. It can be found here: http://xmlsoft.org/XSLT/downloads.html
Newer versions generally contain less bugs and are therefore recommended. XML Schema support is also still worked on in libxml2, so newer versions will give you better complience with the W3C spec.
If you have easy_install, you can run the following as super-user (or administrator):
This has been reported to work on Linux, MacOS-X 10.4 and Windows, as long as libxml2 and libxslt are properly installed (including development packages, i.e. header files, etc.).
If you want to build lxml from SVN you should read how to build lxml from source (or the file doc/build.txt in the source tree). Building from Subversion sources or from modified distribution sources requires Cython to translate the lxml sources into C code. The source distribution ships with pre-generated C source files, so you do not need Cython installed to build from release sources.
If you have read these instructions and still cannot manage to install lxml, you can check the archives of the mailing list to see if your problem is known or otherwise send a mail to the list.
For MS Windows, the binary egg distribution of lxml is statically built against the libraries, i.e. it already includes them. There is no need to install the external libraries if you use an official lxml build from PyPI.
If you want to upgrade the libraries and/or compile lxml from sources, you should install a binary distribution of libxml2 and libxslt. You need both libxml2 and libxslt, as well as iconv and zlib.
The system libraries of libxml2 and libxslt installed under MacOS-X tend to be rather outdated. In any case, they are older than the required versions for lxml 2.x, so you will have a hard time getting lxml to work without installing newer libraries.
A number of users reported success with updated libraries (e.g. using fink or macports), but needed to set the runtime environment variable DYLD_LIBRARY_PATH to the directory where fink keeps the libraries. See the FAQ entry on MacOS-X for more information.
A macport of lxml is available. Try port install py25-lxml.