I have windows xp on both of my computers, but I want to install Linux on one of my computers. One is connected to the internet and the other one is not. The computer that I want to install the Linux onto is 500MHz, with 256 Megs of memory, and a 20 gig hard drive. What I would like to know is what Linux system would work on this, and where can I get the software to install onto this computer.

DSL and many of the other lightweight distros will work

In case you missed it this might help you decide
http://www.bleepingcomputer.com/forums/topic41001.html

DSL, TinyMe, and even some of the "bigger" might work since you have 256mb mem.

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W.B. BlackSpyder

There is a ubuntu version without all the handy graphical user interfaces i belive

Xubuntu and fluxbuntu

I run Xubuntu on an ancient machine that's not even as powerful as the original posters. Methinks Xubuntu would be a good fit.

A good place to look, find, all the above is http://distrowatch.com/ . I suggest you pick 3-4 (or more) and try them out and see which seems to suit you and what you want to do Nice thing about Linux is most (almost all) are free to download so try as many as you are willing to spend time downloading and burning to cd. I've used/tried 8-9 different distros before I settled on this one so don't be afraid to experiment some as most can be used "Live" which doesn't do anything to your system settings and runs from the cd itself, not the hard drive. ( I've got 4-5 distros I play with "live" from time to time ) Plus running them live will tell you pretty quick if your system will handle it well or not.

Once you settle on a distro, most of the applications a distro has immediate access to is in it's repositories. A repository is a library on your computer of links to the Internet of available programs. When you would like to install them, it is downloaded and installed.

Ubuntu's repository manager is called Synaptic Packet Manager.

LUV the Synaptic