First download and setup docker on target server.  My current setup is Ubuntu 17.04 virtual machine run through VMWare

Setup docker to run automatically on startup

docker run -it --restart=always --name teamcity-server-instance -v /opt/teamcity/data:/data/teamcity_server/datadir -v /opt/teamcity/logs:/opt/teamcity/logs -p 8111:8111\njetbrains/teamcity-server

Use Docker pull to get the latest version

docker pull jetbrains/teamcity-server

List all docker images

docker images -a

Stop the TeamCity container

docker stop teamcity-server-instance

Delete the container

docker rm CONTAINER_NAME

Delete the old TeamCity docker image

docker rmi IMAGE_ID

Restart the docker container now with the new image for the container

docker run -it --restart=always --name teamcity-server-instance -v /opt/teamcity/data:/data/teamcity_server/datadir -v /opt/teamcity/logs:/opt/teamcity/logs -p 8111:8111\njetbrains/teamcity-server