First of all, let me correct your terminology: you meant GNU/Linux when you
wrote Linux. And, yes, it matters.
Then, you really need to know that installing/removing application is mainly
(or even exclusively for people with no special need) achieved through the
package manager. Synaptic is an excellent graphical interface to it.
tikz-cd does not seem to be available in the repository. Probably because it
is a very recent project. However, you can simply download the .sty file and
save it in the directory where you compile the document requiring it. If you
want tikz-cd available for all your documents (and not copy it every time),
you can. By default, you just need to save it in a "texmf" directory that is
directly inside your home directory (i.e., ~/texmf).
Notice that tikz-cd requires pgf that you can install from the package
manager.
