you would have your modem connected to your internet connection (cable for example). You would run an ethernet cable from the modem to the router. You would then run another ethernet cable from the router to your desktop.
Assuming you use a standard setup routine (would come with the router) you would then have internet at your desktop. You would need to configure the router for security and wireless which isn't that difficult. Once you're wired up to the router at the desktop, you would go to a browser (like Internet explorer) and type in http://192.168.0.1 or http://192.168.1.1 (depending on the router brand) and you would then be able to set up wireless.
You will want to have some security in place like WEP or WPA security which would require that you enter a code or key into any device that you want to run wirelessly off the router. You will want to set up a password for the router so no one can sneak in and change your settings or gain access to your system.
A good router would cost you about $90.00 or less.