For question 1 (see two computers each other): you need to make sure that both computers have the following two services enabled:
Client for Microsoft Networks
and
File and Printer Sharing for Microsoft Networks
You can check this in Control Panel -> Network Connections -> Local Area Connection -> Properties. On the top part of the window, you should see these two listed and checked, in addition to Internet Protocol (TCP/IP). If not, click on Install button and install them.
For question 2 (using mstsc to access your home computer), you first have to have Windows XP professional version on your home computer because remote access is a feature on that version of Windows XP (unless you have terminal service running), and enable it. I don't want to get into the details, you can check this out yourself:
http://www.microsoft.com/windowsxp/using/mobility/getstarted/remoteintro.mspx
Even if you have this done, I don't think it will work immediately. You have to first check your organization that they allow your computer at work to access the outside computer (their firewall may block such access in the first place). If this is ok, then you have to open up your router at home to forward such access to your desktop (it's called port-forwarding, check your router manual about how to do that). And you need to find which port(s) MS remote service is using to set up your router (sorry I don't know that). And also set up your software firewall to all this access too. And lastly, if you don't have a static ip for your home network (most of the ISPs usually only give you dynamic IP) you still have an issue reaching your home PC from your organization because the ip may change from time to time. I remember there are solutions for that using some kind of free ip monitoring service, I just don't have in my my head now. You can do a google search for dynamic ip monitoring for such information