I have followed the docker installation doc for installing it on my machine which is a 32 bit machine running Ubuntu 12.04
The step
$ sudo apt-get in
there has been some hacking, unsupported ways to do so, see
http://mwhiteley.com/linux-containers/2013/08/31/docker-on-i386.html
Keep in mind that the previous link was in August 2013, I am not sure you will be able to do the same with the latest versions of docker.