Normally a PC can't accomodate multiple users with a direct connection. What those machines probably use is an adapter card designed to allow simultaneous access, they're essentially a network controller with a video chip on it (and possibly a very low speed CPU), that sends the data out to a breakout box that connects your monitor and keyboard/mouse so they act like an old dumb terminal for a mainframe, but with better graphics. AJump doesn't seem to sell the adapters and software separately, unless they just don't have a description or category for it that I can find.
You can't make the "extra" machines work as well as they would if they were fully separate. You can't get any 3D performance due to the low-quality video chip, and any connected machines are sharing the CPU, memory, and hard drive data rates, and you can't get sound for each individual machine very easily I bet. Luckily since the dumb terminal is only receiving low-resolution video and sending keyboard/mouse signals, the bandwidth limitations don't cause too severe an issue.
Here is one example.
This place seems to sell the newer version of the above device. It seems the original company went out of business.
There used to be several products like this available. It seems hard to find them right now. They are somewhat expensive compared to getting a full computer (you can get a machine for 200 bucks that would give you better performance than a shared machine), and the advantages of sharing a single machine are probably outweighed in most cases by the disadvantages and comparison to unshared full computers. The software licenses are the primary cost savings you might see from sharing a computer, since you only need one OS.
WindowsXP of course also includes terminal service software (Remote Desktop), however it normally only lets one user use the machine at a time. When someone else logs in remotely, it locks the local machine. The software that comes with the sharing adapter cards is basically a terminal server software that doesn't limit the connections, so the operating system sees the adapter as a "remote" computer making a connection to it.