You have only 1 PCI-E x16 slot, so you'll be limited to one video card.
Because of this, your only option is to get an Eyefinity Radeon card, which are very expensive and will require at least one NON passive Display Port converter. (Like this: http://www.accellcables.com/products/DisplayPort/DP/mdp_vga.htm
An example video card to accomplish this:http://www.newegg.com/Product/Product.aspx?Item=N82E16814150494&cm_re=eyefinity-_-14-150-494-_-Product
You'll need to connect two monitors via the DVI (use DVI to VGA adapters if you need to) ports and for the third monitor use the NON passive display port converter. If you use a passive one, it WILL NOT work.
Problem is that this video card won't run on your current power supply. You'll need to upgrade your power supply in every solution, as more modern video cards have a very high power demand. You're looking at spending at least $400-$450 including tax and shipping, for the PSU and GPU. This doesn't include the cost of the converter, which you'll have to have.