Docker on Ubuntu - not working

Today I've installed Docker into my Ubuntu Linux 15.04 according to official documentation (note here: after installation I've executed  sudo usermod -aG docker <my_username_here> because I want to execute Docker as a non-root user).

However, when I tried to do docker docker run hello-world I got:

ernestas@ernestas-VirtualBox:~$ docker run hello-world
Post http:///var/run/docker.sock/v1.20/containers/create: dial unix /var/run/docker.sock: no such file or directory.
* Are you trying to connect to a TLS-enabled daemon without TLS?
* Is your docker daemon up and running?

Not good, right? So, I solved it by:

sudo service docker start

And then docker run hello-world - worked!