The only official and legal way to search the texts of the Thesaurus Linguae Graecae database is via the TLG Online web interface. There is an abridged version of the database available for no cost, and some of the tools (dictionaries etc.) are likewise open access, but full access to the database requires you either to be on-site with decent web access at an institution with a site license, or to purchase an individual license. The resources on the TLG website are some twenty years more up-to-date than the last CD-Rom that was published in 2000, and the in-house search tools are more sophisticated than more of the third-party software that was used in the past to access the CD-Roms.
The PHI Greek Inscriptions database is also online at Searchable Greek Inscriptions, which serves the text of inscriptions from the Cornell and now Ohio State databases. Texts are browseable by geography and bibliographic series, and there is a powerful but basic raw text search function. The online database is presumably more up to date than the 1996 CD-Rom.
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
For other tools to search in the texts of inscriptions and papyri, see the Epigraphy and Papyrology category in this Wiki.
to be continued