Okay, first, do NOT install IPX/SPX or any other protocols.  The default TCP/IP connection is all you need and want.  Your router should be assigning your machines their IP addresses and putting them into the same subnet automatically; you generally don't need to worry about that.

Next, for convinence, make sure both PCs are in the same workgroup.  Right-click My Computer, go to Properties, and Network.  Make sure both have the same name.

Now, on the XP machine, you may have the firewall enabled, which will prevent any machine from connecting to it.  You'll want to turn it off for the time being (when you update XP to Service Pack 2, you'll have better control over the firewall, and can reenable it then).  Go to Control Panel, Network Connections, right click on Local Area Network, and go to the Advanced tab and uncheck the firewall.

Then, you need to enable the Guest account on the machine that you're sharing.  Control Panel, User Accounts.

Next, choose a folder to share, right click, Sharing, give it a name, and add "Guests" to the user list.  You can choose Read Only or Make Changes/Full Control.  If you are not running "Simple File Sharing" on XP, you'll also need to go to Security and grant rights to the Guests account group.  No need if Simple File Sharing is enabled.

Okay, so now you should be able to go to the other machine and see your shared folder.

-Troy

Did you verify that both machines were getting an IP address, and that they were on the same IP subnet with the same subnet mask?

-Troy

Hmm...  When all else fails, delete the network card drivers and let them reinstall.  Restoring their default settings will usually fix it.

-Troy

Depends on the router, but probably not.  What you'll probably need to do is assign your "server" machine a fixed IP address, and then assign that address to your DMZ in the router.

Most home routers allow you to choose one PC to be in the "DMZ".  What this means is that anyone going to your cable/DSL modem's IP address will get routed to that PC, as if your router didn't exist.  However, all of your other machines will still be able to get out to the net using the same IP, and will be unseen from the outside world, just like they are now.

Usually, your router will be set to assign a certain group of addresses to your computers via DHCP, so you can just plug them in and they'll get an IP address automatically.  Typically, this range is 192.168.1 with the last octet being 100-255.  This leaves you 100 manually-assignable IP addresses (0-99) for machines that need a fixed (i.e., static) IP address.  Your router may use a different range, so check your docs.

Generally, you just need to pick an IP, say 192.168.1.10, and enter that into your "server's" IP configuration, along with a subnet mask of 255.255.255.0.  Then, put the same (192.168.1.10) IP address in your router's DMZ setting.  That should allow the outside world to access your server.

Of course, you must be very careful to lock down and secure your server before you expose it to the world, because it will be vulnerable to the constant attacks that go on all day and all night.  If unsecured, it would be a great way in to your private network...  

-Troy