If your version of Kitsu is hosted and maintained by CGWire, you don't have anything to install. Simply, connect to the URL that was given to you to start using Kitsu!
To run properly, Kitsu requires Zou, the database API. Information related to both modules installation are located in the Zou installation documentation.
If you have technical skills, you can run Kitsu / Zou through Docker to give it a try:
docker run -d -p 80:80 --name cgwire cgwire/cgwire
Then you can access to Kitsu through http://localhost