On your motherboard you will generally find one or two long PCI-Express slots. These will be the longest physical slots on the board.
When only one graphics card is in use, it gets the full "16x" speed from the motherboard. The other long slot goes into 1x mode, allowing you to use it with smaller 1x PCI-Express cards such as sound cards or network cards. The slots are designed so that cards designed for small slots can also fit into larger ones, but not vice-versa.
If your board has two of the longest slots, then you can probably use two graphics cards. Each card gets 8x speed from the motherboard. You may have to change a switch or flip a small circuit board on the motherboard to get it into "dual video card mode".
The original intention of this design was for nvidia "SLI" mode. This allows two graphics cards to drive one monitor, theoretically doubling display performance.
What you want however, is to drive three monitors. In this case, you need to ignore any option of "SLI" mode in your graphics card drivers. I recommend you buy your second card from the same chipset manufacturer as the existing card eg. nvidia + nvidia. This means you only have to run one set of drivers on the PC.
Things get problematic if you only have one 16x long PCI-Express slot. The other slots on the board will likely be only 1x (smallest) or 4x (slightly larger) PCI-Express slots, or even old PCI slots. In this case, you will have to get either a PCI-Express 1x card such as one from Matrox, or a PCI version of, say, an nvidia card.
The matrox card is likely to perform better in 2D than a PCI based card, but may confuse windows with having both nvidia or ATI drivers and Matrox drivers installed.