Sorry - I did not see your post until just now.
I would suggest buying a Belkin Wireless G router. They are about $40 at Walmart and very easy for a non-geek to set up. Assuming that you currently have a desktop that is connected to your modem, you will connect that desktop to the router. For the new desktop, you will need to purchase a wireless G USB adapter. Again I would stick with Belkin.
When you set the router up, make sure that you turn on WPA2 encryption. As part of the set-up of the WPA2 you will be asked to provide a password. Use something difficult for the password. Do not