The previous post mentioned that Docker provides CE packages for Ubuntu. For users of Debian, SLES, RHEL, Fedora, ClefOS, openSUSE, and Alpine, there is still an option to get the latest Docker CE version to their environment:
https://download.docker.com/linux/static/stable/s390x/ contains static builds of docker. Downloading the tarball, extracting the binaries into /usr/lib and starting them manually is sufficient for getting it up quickly. Docker documents these steps on their webpages.
Statically built binaries do not depend on any libraries on the host system. That allows to build executables that will work essentially on any Linux flavour with a decent kernel -- which is the case for the current versions of the major distributions.
To fully integrate the binaries into the Linux environment, an integration into systemd (or whatever your distribution of choice uses) makes sense. https://docs.docker.com/engine/admin/systemd/#manually-creating-the-systemd-unit-files hints to according systemd unit files.
Update 2017/10/12: the systemd-related related page on docs.docker.com page (linked to above) has changed. To integrate with systemd, copy the files docker.socket and docker.service from https://github.com/moby/moby/tree/master/contrib/init/systemd to /etc/systemd/system .