TSE requires PHP 4 various libraries listed below, and the external program agrep. On a reasonably recent Unix system this shouldn't be a problem, but your mileage may vary. All the PHP libraries are included in the distribution, the only thing you may have to worry about is whether your version of PHP has the XSLT extension. If you are going to set up an LSID authority you will need Perl and IBM's LSID code (available from SourceForge).
PHP 4 or later is needed, together with the xslt extension (I've no experience with PHP 5). On Mac OS X I use the package provided by Marc Liyanage.
If PHP doesn't have the XSLT extension (e.g., PHP 4.2.2 installed on Red Hat Linux 8) then we need to do the transformations using the Sablotron command line program sabcmd. That means installing Sablotron. Make sure you have libiconv installed before installing Sablotron so that ISO-8859-1 character encoding is supported, as this character is required by the Perl bp import routines. Linux users should already have this, but Mac OS X users might need to install it (10.3 has it, but earlier versions don't).
TSE depends on a mixed bag of PHP libraries, all of which are packaged in the TSE distribution. These files are listed here if you want more recent versions, and also to give credit to the authors of these packages.
The Perl scripts for LSIDs require various libraries (see the LSID SourceForge site for details), which can be grabbed from CPAN:
sudo perl -MCPAN -e shell install <library-name-here>
TSE uses agrep to perform approximate string matching. This, together with Google's spelling suggestion web service enables TSE to provide spelling suggestions. See Tom Gries' page on agrep for details. On a Unix box you can just grab the source and compile it.
In order to use agrep you need a list of the correctly spelt taxonomic names, where each name starts on a new line. The TSE distribution contains an example of such a file, called namelist.txt.