Fluid Construction Grammar can be downloaded as part of the Babel software package at this link. Babel is a general cognitive framework that connects FCG with language technologies for conceptualization and interpretation, and with mechanisms for cognitive processing, learning, multi-agent interactions, and robotic embodiment.
The technical documentation for the Babel 2 framework is available here .
As of 2015, a new notation for FCG has been introduced. The details and a few examples can be found in the article ‘The basics of Fluid Construction Grammar’ by Luc Steels, to appear in Constructions and Frames. You can download a draft of the article here.
About Babel 2: Babel 2 is written in Common Lisp and runs in most major Lisp implementations (ccl, sbcl, lispworks) on all major platforms (linux, mac osx, windows). Its source code is released to the public under the BSD License.