There's multiple options for you to support 3 displays.
1. Get an AMD card that supports "Eyefinity". These cards, even by themselves, can drive 3 or more displays (depending on how many ports they have) at once.
2. Get a very high end Nvidia card, or two mid/lower end cards in SLi (that means together, and they have to be the EXACT same card). The newer higher end Nvidia cards (6xx) can support 3 monitors at once by themselves if they have the right amount of ports, but they're extremely expensive.
The cheaper solution is most often the AMD Eyefinity cards. You can find them on Newegg.com or other online retailers, even sometimes in stores like Best Buy, etc, albeit they're overpriced there.
The screens are utilized by the card in multiple ways (read: your choice). You can have them as each individual displays, you can have them all together for one HUGE desktop display, etc.
The only things you're going to want to keep in mind are the power requirements (the higher end the card, the more wattage and amperage it's going to need from your PSU, not to mention the proper PSU connector. The other thing is size and airflow. Make sure your case has adequate space and airflow for the card you're looking at.