Right now I have two computers, a laptop and a desktop that each uses Windwos XP, that I want to transfer files between by putting them onto a network so as to back up everything in the laptop because I will have to reinstall windows in it tomorrow, effectively wiping out everything.

The laptop gets online wirelessly through a NETGEAR WGT642v2 router, however I do not know if that router is capable of LAN at all. If so, how exactly do I get it set up. I've been to a whole bunch of different sites and I've seen a bunch of different ways to do it but I'm not sure I can get any of them to work.

I know it has something to do with putting both computers in a Workgroup and setting files to "share" but don't you need any software or anything to do this?

Hmmm, I don't know that router and there appears to be very little out there in Googleland as well what does your instruction manual say?

All computers to be on a network need to be in the same workgroup.

You will also need to make sure that any software firewalls running on either PC is either turned off (ONLY if the router has its own built-in firewall!) or are configured to make the entire IP address range of the local network visible (e.g. for me this is 192.168.2.1 to 192.168.2.255).

As for sharing files/folders on the network, I can remember answering something along these lines some time ago. Please take a look here for that thread.

If I understand your question correctly, all you want is to back up your data before you wipe the hard drive. Okay, just burn your data to a CD. Even if it takes several CDs, it is far cheaper than trying to set up a home network that could take days if you have problems to troubleshoot. Plus you will have to purchase a wireless NIC for your desktop which will be pricey.
If your lappie doesn't have a burner, you can get a 1gig flash drive for $20 and use that. Even faster.