Search the TLG and PHI databases

TLG Online
The simplest answer to this question is that if you are a member of an institution that has a license to the TLG Online, then (so long as you are on-site and have half-decent web access) that is the best way to search the texts of the Thesaurus Linguae Graecae, both because the search engine is excellent, and because the texts are now several years more up-to-date than the CD ROM.

PHI Greek Inscriptions Online
The PHI "Searchable Greek Inscriptions" tool is also online at http://epigraphy.packhum.org/inscriptions/, albeit with a more basic search interface than the TLG.

TLG/PHI CD ROMs
If you do not have access to the online TLG, however, and therefore want to use the TLG CD or if you are interested in searching one of the Packard Humanities Institute discs of documentary papyri and inscriptions (PHI 7.0) or Latin texts (PHI 5.3), then you should be aware that the CDs on which these texts are served do not contain software with which to read or search said data.

If you run a Windows PC (or a Classics Mac--OS 9 or lower) then many of the software applications listed on the TLG Software Page may be appropriate. Most of these are commercial products that require purchasing, although some are cheap or even cost-free. (Several tools are reviewed in a recent BMCR article at http://ccat.sas.upenn.edu/bmcr/2005/2005-05-07.html .)

There is also a free software package (GPL) called Diogenes, which is not listed on the TLG page. It runs under Mac OS X (10.3 or later), Windows and Linux, and can be set up as a networked server. The installation procedure has been much simplified in recent versions.

MacOSX users may also be able to run the HyperCard software package Pandora using either the Classic system 9.2 emulator, or a HyperCard emulator such as Runrev's Dreamcard (though I should disclose that I haven't managed to make the latter work yet, GB).

Now see also the version of "SNS Greek and Latin" for MacOSX, available from http://snsgreek.sns.it/sns_02.html

Other search tools
For other tools to search in the texts of inscriptions and papyri, see the Epigraphy and Papyrology category in this Wiki.

to be continued