You can check if it has started by running the command ps -ef. You can also grep it to docker if you want to reduce the number of results(using | grep docker). If its of not running, execute
sudo service docker start
OR if it still doesn’t work then
You can refer this link
docker docs
You can run docker run -d or docker run -d & so that you can use the same terminal or even close it if. It will set the value to true, so your container will run in “detached” mode, in the background.
You can also auto start it when your OS starts using update-rc.d servicename defaults or you can also refer to the links below, where you have to give docker as service name and your defaults.
Some more links to refer –
auto start,
upstart
These are different ways of doing it.