This is probably one of the quickest and easiest ways to get Docker and Docker Compose running on the Raspberry Pi.
(Tested with Raspberry Pi B+ Rev 1.2)
After searching the Inter-Webs for hours and having several things not work for me, I decided something needed to be done about it.
curl -sSL https://get.docker.com | sh
sudo usermod -aG docker pi
docker run hello-world
sudo apt-get install libffi-dev libssl-dev
sudo apt-get install -y python python-pip
sudo pip install docker-compose
Important Notice about Docker on the Raspberry Pi
Raspberry Pis use the ARM architecture, and as a result, won't be compatible with all containers out of the box. Images will need to be built from an ARM base image. But, most of these images can easily be found on Docker Hub