(based on https://lists.ubuntu.com/archives/snapcraft/2016-October/001382.html and https://docs.docker.com/engine/getstarted/)
Search for the snap:
$ snap find docker
Name    Version   Developer  Notes  Summary
docker  1.11.2-9  canonical  -      The docker app deployment mechanism
j2      0.3.1-0   cmars      -      Command-line interface to Jinja2 for templating in shell scripts.
Add the docker group:
$ sudo groupadd --system docker
Install the snap:
$ sudo snap install docker
docker (stable) 1.11.2-9 from 'canonical' installed
Connect the interfaces:
$ sudo snap connect docker:docker-cli docker:docker-daemon
$ sudo snap connect docker:firewall-control ubuntu-core:firewall-control
$ sudo snap connect docker:support ubuntu-core:docker-support
Restart the service:
$ sudo service snap.docker.dockerd stop
$ sudo service snap.docker.dockerd start
Verify the installation:
$ sudo docker run hello-world
Unable to find image 'hello-world:latest' locally
latest: Pulling from library/hello-world
c04b14da8d14: Pull complete 
Digest: sha256:0256e8a36e2070f7bf2d0b0763dbabdd67798512411de4cdcf9431a1feb60fd9
Status: Downloaded newer image for hello-world:latest
Hello from Docker!
[...]
Show the containers in the system:
$ sudo docker ps -a
CONTAINER ID        IMAGE               COMMAND             CREATED              STATUS                          PORTS               NAMES
cbcdc2e117ff        hello-world         "/hello"            About a minute ago   Exited (0) About a minute ago                       insane_brahmagupta
Run bash in an ubuntu container:
$ sudo docker run -it ubuntu bash
Unable to find image 'ubuntu:latest' locally
latest: Pulling from library/ubuntu
6bbedd9b76a4: Pull complete 
fc19d60a83f1: Pull complete 
de413bb911fd: Pull complete 
2879a7ad3144: Pull complete 
668604fde02e: Pull complete 
Digest: sha256:2d44ae143feeb36f4c898d32ed2ab2dffeb3a573d2d8928646dfc9cb7deb1315
Status: Downloaded newer image for ubuntu:latest
root@c72005d1b090:/# apt install update
root@c72005d1b090:/# apt install -y lsb-release
[...]
root@c72005d1b090:/# lsb_release -a
No LSB modules are available.
Distributor ID:	Ubuntu
Description:	Ubuntu 16.04.1 LTS
Release:	16.04
Codename:	xenial
Tested in an ubuntu classic xenial kvm.
Everything works, but there are some denials logged by snappy-debug: https://paste.ubuntu.com/23415131/