GIMP 2.x handles a variety of font formats, most notably TrueType, OpenType and Type1.
Most distributions will propose a large choice of fonts in their package manager. The easier is usually to install them this way.
In case you want to manually add third-party fonts (commercial, downloaded…), adding fonts is usually just a matter of moving font files into a directory that is searched by the font system. Have a look at /etc/fonts/fonts.conf (and perhaps /etc/fonts/local.conf) to find out which directories are searched, or look for your operating system documentation. After copying the fonts there, you should run fc-cache to regenerate the fonts cache.
Some distributions also propose a graphical tool allowing to install fonts from third-party without bothering about the specifics.
Fonts added this way will be available to all applications using the Fontconfig system (such as GIMP).
You might want to install fonts for use with GIMP only or you might not have permissions to install fonts system-wide. For such cases, GIMP 2.x also looks for fonts in a GIMP specific font search path. The default place where GIMP will look for user fonts is ~/.gimp-2.8/fonts/ but you can change it or add other directories by modifying your gimprc or in Edit -> Preferences -> Folders -> Fonts. Then press the Refresh button in the Fonts dialog and start using your new fonts.
This section is mostly informational, for users or developers who want to know more about under-the-hood font handling in GIMP 2.x. In nearly no case would you have to understand and know any of this in order to have font support in GIMP 2.x. See above for adding fonts simply.
Starting with GIMP version 2.0, font rendering is handled significantly differently from the way it was done in GIMP 1.0 and 1.2. GIMP no longer uses the X server to render the fonts. Instead it uses Pango and the FreeType library. Font configuration is handled by Fontconfig. As a result you get much better font rendering with real antialiasing, support for bidirectional text and various scripts.
Fontconfig can nowadays be considered a de-facto standard on Linux and other Unix operating systems as the simple way to list and share the same fonts accross all application. Most modern graphical programs with text support now uses this library. And desktop environments (GNOME or KDE for instance) use it too. Therefore it is likely already installed and properly set up out of the box in most Unix/Linux machines and you have probably nothing to do in particular to have fonts working in GIMP 2.x.
If you use a very raw operating system though, or if you simply want to know more, you may want to have a look at the Fontconfig User Manual to create or edit your font configuration file. Note though that since it is such a widespread system, modern desktops environments such as GNOME or KDE, or other distribution software, may overwrite your font configuration file. They sometimes provide an easier interface to manage your fonts instead. For this reason, you are advised to search the specific documentation of your operating system distribution before updating your font configuration.