Docker is a very neat tool, and there's a good guide on the Docker website to installing it in Ubuntu, but I always find it's just slightly more cumbersome than this guide suggests.

So here's a quick guide to all the commands I find I have to run to get it working:

sudo apt update && sudo apt install wget  # Install wget just in case you don't have it
wget -qO- | sh    # Install docker - NB: doesn't actually start the docker service
sudo usermod -aG docker `whoami`          # Add yourself to the docker group
# Now log out and back in again
sudo service docker start                 # Make sure the docker service is running

You should now be set to go, unless you're inside a corporate network that doesn't let you use public DNS servers. You can test this with:

docker run ubuntu /usr/bin/apt update

If the above command produces a connection error, follow my guide to fix Docker networking.