We are working at a more polished manual and user guide. A complete language reference is available and is continually updated. It also contains sections pertaining to simulation and usage. We are working on a tool section. If you use Kappa, please cite this document as
P. Boutillier, J. Feret, J. Krivine, and W. Fontana. The Kappa Language and Tools (version of <insert date on cover>), kappalanguage.org.
An older reference manual is available as an online html version. Manuals that are less tightly curated are available in pdf with the stable releases. Since the syntax has changed somewhat, consider the new version even as it is catching up with all the material.
Jean Krivine's teaching page provides some material to get started with KaSim.
You can use KaSim as an OCaml library. Here is the API.
KaSim also exists as a REST service, called WebSim. Here is a description of its HTTP commands.