At a bare minimum, you'll need the following for both the buildmaster and a buildslave:
Buildbot requires python-2.4 or later.
Both the buildmaster and the buildslaves require Twisted-2.0.x or later. It has been tested against all releases of Twisted up to Twisted-2.5.0 (the most recent as of this writing). As always, the most recent version is recommended.
Twisted is delivered as a collection of subpackages. You'll need at least "Twisted" (the core package), and you'll also want TwistedMail, TwistedWeb, and TwistedWords (for sending email, serving a web status page, and delivering build status via IRC, respectively). You might also want TwistedConch (for the encrypted Manhole debug port). Note that Twisted requires ZopeInterface to be installed as well.
Of course, your project's build process will impose additional requirements on the buildslaves. These hosts must have all the tools necessary to compile and test your project's source code.