Is it possible to install joomla on a windows server and what might be the difficulties of going about and doing so. Our client has a windows dedicated box and they want joomla placed on their server.
Yes, it is possible - see http://www.joomla.org/technical-requirements.html
The page that Tadeck referred to, http://www.joomla.org/technical-requirements.html, recommends you use WAMP which bundles together Apache, MySQL and PHP in one install. Once you've installed that the Quickstart Guide will help you (though it talks about using XAMPP, but the previous page says it isn't for live sites). You basically unzip the Joomla install to a directory, and then go to the URL http://localhost/joomla15 to finish off.