I have a desktop with Windows XP and have just ordered a new laptop that will
have Vista.  Can I network these two?

Yes. This how to may help.
Vista Network Sharing
      Vista Network Sharing. Enable Vista simple file sharing · How to
access a sharing printer in Vista ... How to check or setup Windows Vista
home network ...
      www.howtonetworking.com/vista/networksharing.htm


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Hi
Assuming that you have a Router. When the two computers can talk to the same
Router and use the internet you have already a Network.
In order to share resources internally over the LAN, you need to configure
each computer's sharing.
Make sure that the Software Firewall on each computer allows free local
traffic. If you use 3rd party Firewall On, Vista/XP Native Firewall should
be Off, and the active Firewall has to adjusted to your Network IP numbers
on what is some time called the Trusted Zone (consult your 3rd Party
Firewall instructions.
General example, http://www.ezlan.net/faq#trusted
Vista File and Printer Sharing-
http://technet.microsoft.com/en-us/library/bb727037.aspx
Windows XP File Sharing -
http://support.microsoft.com/default.aspx?scid=kb;en-us;304040
http://support.microsoft.com/default.aspx?scid=kb;en-us;304040
Printer Sharing XP -
http://www.microsoft.com/windowsxp/using/networking/expert/honeycutt_july2.mspx
Windows Native Firewall setting for Sharing XP -
http://support.microsoft.com/kb/875357
Windows XP patch for Sharing with Vista -
http://support.microsoft.com/kb/922120
Jack (MVP-Networking).

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Yes!You can do that with crossover network cable.
You must set both computers i same network workgroup and share some folders.
Another way is built small home network using wireless network router.
I have something like that.
Desktop,cabble internet modem,laptop with wireless network adapter and d
link Dl-524 wireless router.
Desktop is conected thrue network cable in Dl-524.Cablle internet modem is
conected thrue network cable in Dl-524 too.Laptop is conected thru wireless
adapter in Dl-524.I can conect another 3 devices with network cable ( second
desktop,network printer ect) and 10 devices with wireless network adapter.
All devices are part of my home network and all can access internet and
other devices.
It works with Windows XP,Vista,Windows 7 and linux without problems.
Dl-524 costs i my country ( serbia ) less than 50€.

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