wget http://download.aircrack-ng.org/aircrack-ng-1.1.tar.gz
tar -zxvf aircrack-ng-1.1.tar.gz
cd aircrack-ng-1.1
make
make install

It very much depends which Linux distribution you're using. I'm going to assume that you're using Ubuntu, given that it's the most popular GNU/Linux distribution at the moment.

The package manager that Ubuntu uses is called APT - Advanced Packaging Tool. It originally comes from Debian (from which Ubuntu is derived) and is also found in Linux Mint (which is derived from Ubuntu).

The three main commands that you need to know are:
(i)sudo apt-cache search package_name
-- Searches the repositories and returns any matching results. Useful if you don't know the exact name of the package that you're looking for.

So, in this case, we might run:
sudo apt-cache search aircrack

Assuming aircrack-ng is in the repositories (I'm not running Ubuntu, so I don't know) it will appear in the list.

The next command:
(ii) sudo apt-get install package_name
Assuming its just called aircrack-ng, we run
sudo apt-get install aircrack-ng

If somehow we realise that we've installed the wrong package or no longer need a particular package we can run

(iii) sudo apt-get remove package_name

Further reading:
http://manpages.debian.net/cgi-bin/man.cgi?query=apt-get&apropos=0&sektion=0&manpath=Debian+6.0+squeeze&format=html&locale=en
https://help.ubuntu.com/community/AptGet/Howto

If you're using a different distribution the answer can probably be found in the documentation. If you get stuck, ask again.

I do hope that you're not planning to do anything naughty with aircrack-ng...