start TeamCity server as docker container

docker run \
-v team_city_data:/data/teamcity_server/datadir \
-v team_city_logs:/opt/teamcity/logs  \
-p 8111:8111 \
-d jetbrains/teamcity-server

start TeamCity agent without docker volume mount

docker run -e SERVER_URL="http://public-ip:8111"  \
-v team_city_agent_config:/data/teamcity_agent/conf  \
-d jetbrains/teamcity-agent

start TeamCity agent with docker volume mount

docker run -e SERVER_URL="http://public-ip:8111"  \
-v team_city_agent_config_two:/data/teamcity_agent/conf  \
-v /var/run/docker.sock:/var/run/docker.sock \
-v /usr/local/bin/docker:/usr/bin/docker \
-d jetbrains/teamcity-agent

NOTE: for docker mount to work and docker commands to be executable inside the container, you need to set less stricter permission on docker on the host with the following command

chmod 666 /var/run/docker.sock