A worked example, backporting cmake from Ubuntu 12.10 (quantal) to Ubuntu 12.04 (precise). You’ll need to install apt-src using your package manager of choice.
Add the source deb repository
Create an apt source list (the name isn’t important, but I gather it must have a .list extension):
sudoedit /etc/apt/sources.list.d/quantal.list
and add the following line (edit to taste):
deb-src http://ie.archive.ubuntu.com/ubuntu quantal main universe multiverse restricted
Then update apt-src:
sudo apt-src update
Get source and build
You don’t have to be root to build; just make a directory, say:
mkdir ~/quantal-backports && cd ~/quantal-backports
Install source:
apt-src install cmake | tee apt-src-install.log
And build:
apt-src build cmake | tee apt-src-build.log
Install packages
Assuming no errors, the output of the build process is one or more .deb packages. Install them like so:
sudo dpkg -i cmake*.deb
And you’re done! (Well, maybe dpkg fails because of missing dependencies; in that case, apt-get those manually, or read the Debian docs about ‘Using APT locally’)