The easiest way for writing with that class would be if you would place the class file (or even all files from the zip archive you linked) into the same directory as your own article. Just to mention a quick way if you just use it once.
If you actually would like to install it, an explanation may be a bit longer, depending on your experience. It would mean putting the class file(s) to your user TeX home directory (such as C:\Users\stefan\texmf\tex\latex\amcs\) or into the computer's local directory structure (C:\Program Files\MiKTeX 2.9\texmf\tex\latex\amcs\), and refreshing the file name database (Start/ All Programs/ MiKTeX/ Maintenance/ Settings, the "Refresh FNDB" button).
Perhaps have a look at
Local Installation of Class Files.
Stefan