The package is in Quicklisp; source is available on github. If you want to download it from the latter, your best bet is cloning it from the repository, for which you need to install Git. Then go to the directory where you want it placed (a subdirectory will be created within it, so you don't have to do it), and use
git clone git://github.com/rpav/cl-cairo2.git
You might have to create a symlink to the asd file in your ASDF
systems directory. After that, just use
git pull in the subdirectory to update. A lot of guidance on Git is available here.
The package contains a tutorial. Patches and bug reports are always welcome. You can also refer to the cairo website for other documentation/tutorial.