What You Need
Assuming you already have a monitor for your system, you need three more. In general, I recommend buying four monitors of the same make and model, which helps eliminate annoying differences in color balance or brightness. At the very least, they should all be of the same size and resolution. To give yourself the most flexibility in making connections, choose displays that accept both DVI and VGA (though you likely can get cables or adapters that will allow you to work out any combination of interfaces).
You'll also need a stand for the monitors. You can find models that string out four panels in a single line (which fans of flight-simulator games tend to love because of the wide, panoramic view). I prefer a two-by-two matrix; with such an arrangement, I don't have to turn my head as much to see any part of the combined display. For my setup, I chose the Ergotron DS100, which lets you easily angle the monitors for better ergonomics.
One key point: Ensure that your monitors match the mounting holes for the stand. Most stands use the VESA standard mount patterns, but you can't just assume that a given mount-and-monitor combination will pair correctly, so be sure to read the specs of displays and stands carefully before you buy anything.
Most graphics boards these days come with two DVI display connectors. If that's what you have in your system, you'll need to buy just one more dual-headed card to support four monitors in all. If your system has only one display connector, you'll have to pull out that board and install two dual-head boards. Make sure that you have sufficient expansion slots available in your PC, and that you buy a board or boards that match that type of slot. (If you don't have available slots, or you don't want to bother opening your computer's case, you still can have a multiple-monitor installation; see the final section of this tutorial.)