First of all, it's called KDE. You don't really have to uninstall your current desktop environment (no matter what it is, Cinnamon, Xfce or whatever), instead, you can install and run multiple desktop environments in a single operating system (which is Linux Mint 15 for you). Below I'll fully explain how to install KDE on your system.
1. You need to ensure that you have at least 830MB of free space on your hard drive, as KDE requires you to do so.
2. You need to open up Software Manager. You can find this in Menu.
3. Search 'kde' in the search box and you should probably have KDE in the first listing.
4. Now you can install it by clicking on the install button. Once it's finished, close all windows and log out.
5. Can you see the 'Session' button right next to the United Nations flag? Click that, and it will show you all the available desktop environments.
That's it. You now have KDE installed. If you don't like it, you can install any other desktop environments as you wish. I hope this was helpful.
