I've already read through Kubernetes tutorials. The problem is the lack of a straight answer on how to get a Kubernetes image for TeamCity into a plain Kubernetes instance.
My install doesn't use Google Cloud engine, Amazon EC2, or Azure, which means I can't use their built-in container registries.
This site appears to recommend installing docker and using it the pull the container image: https://hub.docker.com/r/jetbrains/teamcity-server/
This GitHub page appears to imply that a specific plugin is required for kubernetes: https://github.com/JetBrains/teamcity-kubernetes-plugin
The Rancher Web UI has a JavaScript/HTML form to install containerized apps: "Enter the URL of a public image on any registry, or a private image hosted on Docker Hub or Google Container Registry."
-> I found teamcity-server on Docker Hub, although I have no idea if I can just give it the page (https://hub.docker.com/r/jetbrains/teamcity-server/) or if there's a special subpath that I have to give it.
For the Docker Hub, the "Enter the URL" instructions are wrong and actually fail with an error. To use the Docker hub, you just type the repository name.
For example, to use teamcity-server: https://hub.docker.com/r/jetbrains/teamcity-server/
you would type (as the app URL): jetbrains/teamcity-server