This is what an ethernet cable looks like. The connector looks much a telephone connector, but is wider and has more pins.
Okay, I think I have it all figured out. My internet connection is called a “network connection” XP’s control panel, so I figure I must, indeed, be using a network card, and so I figure I will, indeed, be able to do this crossover cable thing.
One last question: Does it matter that the two machines will have different versions of windows? (Current == XP, new == Vista)
Oh, also: What about the fact that some of the files on my current computer are in “my documents” folders indexed to particular user accounts? Some of those files accounts are only accessible when one is logged in under the corresponding account, correct? How will that be handled by the network connection?
-FrL-
If you log in as administrator, you can see all the user folders. Optionally copy them all to some non-My Documents place on the old machine to consolidate, then copy the whole kaboodle to the new machine. If you want the same user accounts on the new machine, you’ll need to make all those accounts, find all the new user folders, and copy all those saved documents into them.
Shouldn’t.
Just to really scare the crap out of you, here’s MS’s help page on file sharing. It’s not (usually) as bad as it looks, and that page is intimidating because it’s far too detailed.
Oh wait.
Shoot.
Do both machines need to have monitors in order for me to be able to do this?
Or I guess I could switch a single monitor from one to the other as needed?
-FrL-
Nope.
Okay, I’m just trying to figure out how to assign them both IP addresses, but I guess I can do that from a single machine?
I’m sure this will all become clear to me once I’ve got the actual setup going.
The great thing is, my current computer actually has two LAN cards in it due to a long-ago comedy of errors. So I can probably be online at the same time as I’m trying to get this crossover cable thing going. So I can pester you guys some more. Thanks! 
-FrL-
She’s not paranoid. She’s smart. Your hard drives will fail, it’s only a question of when. Then again, not all CDs and DVDs are created equal, and some will fail much earlier than others, with the worse recordable media failing in about 5 years.