I go to a school that only has wireless internet. My desktop doesn't have a wireless card. I do have a wireless router (netgear wgt624 v3). I was wondering if I could use the router to receive the wifi and distribute it though ethernet somehow. Is this posisble?
Sorry, no. The Wifi specification makes bridging through a client connection an illegal configuration and the factory firmware slavishly adheres to the specification. You'd need to run aftermarket firmware to get around that restriction using a "client bridge" or "WAN on Wifi" mode. I don't believe the version 3 hardware is supported by any aftermarket firmware.
If you can find aftermarket firmware (Tomato, OpenWRT, DD-WRT, and so on) that works on your hardware, you should be able to make it work. Just use a client bridge or WAN on Wifi mode.
Most likely, the best solution is just to get a cheap USB Wifi adapter. You can also use a Wifi station adapter that adapts Wifi to Ethernet -- however that's best for things like gaming systems or embedded systems, it's an inferior solution for a PC.
There are wireless adapters that can plug into your desktop. Most suppliers of network adapters, such as Netgear and D-Link, have these. Here are some examples:
This one plugs directly into a PCI slot: http://www.dlink.com.au/products/?pid=790
And this one plugs into a USB port: http://www.belkin.com/IWCatProductPage.process?Product_Id=179211