I have set up several VPN's for clients, so I'll try to field this:
If you are looking for casual file sharing and remote access on an occasional basis, you have everything you need in WinXP. You won't have much in the way of a secure connection, but you should be able to share and control sharing from each other's computer. You can even remotely control each other's computers with permission (al a PC Anywhere). You will need to know each other's IP's. This is certainly the cheapest way to go. You can get information on setting this up at Microsoft's Knowledgebase site.
You might want to consider a VPN if you want a persistent, secure connection where you want access to each other's machines at all hours. Of course, both machines would need to be powered up at all times. It also helps if one of you has a static IP to act as the 'server.' When using a VPN, your 'clients' will look just like other nodes in your Network Neighborhood (just as if they were connected to a local hub/switch).
There are both software and hardware solutions for setting up VPN's. Personally, I haven't set up a software VPN in quite a while because the hardware solutions have hit rock bottom prices. Software solutions usually require a separate machine to act as server and need a fair amount of administration. The hardware solutions are much cheaper and simpler to use.
I have set up several SOHO clients with the Linksys BEFVP41 broadband router. This is essentially the same product as the popular BEFSR41 broadband router with a 4-port switch, but the BEFVP41 includes a 70-tunnel VPN server. The price is right at $180 List/$150 street (you can find the BEFSR41 on sale for about $70). Your post infers that you are simply trying to set up a peer to peer network, but you would only need one BEFVP41 to act as 'server.' The 'client' would need to set up Point to Point Tunneling Protocol (PPtP) and preferably IPSec(urity) on their end. If you are already using a broadband router, both these protocols are built in. I am assuming that you both have some sort of broadband connection. Attempting to set this up on a dial-up can be excruciatingly slow since VPN's require some extra overhead. The Linksys product has pretty good documentation to help you set it up.
For more information, see PC Magazine articles:
"Safe Passage," September 25, 2001 (VPN)
"Broadband Routers," February 12, 2002 (Broadband hardware)