I installed docker on a Debian 7 machine in the following way
$ echo deb http://get.docker.io/ubuntu docker main > /etc/apt/sources.list.d/docker.list
$
Check that you have free space on /var as this is where Docker stores the image files by default (in /var/lib/docker).
First clean stuff up by using docker ps -a to list all containers (including stopped ones) and docker rm to remove them; then use docker images to list all the images you have stored and docker rmi to remove them.
Next change the storage location with a -g option on the docker daemon or by editing /etc/default/docker and adding the -g option to DOCKER_OPTS. -g specifies the location of the "Docker runtime" which is basically all the stuff that Docker creates as you build images and run containers. Choose a location with plenty of space as the disk space used will tend to grow over time. If you edit /etc/default/docker, you will need to restart the docker daemon for the change to take effect.
Now you should be able to create a new image (or pull one from Docker Hub) and you should see a bunch of files getting created in the directory you specified with the -g option.