The default docker data folder is /var/lib/docker. This can be changed to another folder with the following steps. These all need to executed as root or with sudo.
Stop Docker on your computer
service docker stop
Create a new docker daemon config
Add the following text and replace /mnt/docker with the path you want to use as the docker data folder
Save your changes and close the file.
(Optional) If you want to move the existing data to the new folder
cp -rp /var/lib/docker/* "/mnt/docker/"
service docker start
Remove the old folder if everything is working
rm -rf /var/lib/docker