Typically the card needs to have multiple outputs, usually they have DVI with additional HDMI outputs to hook up to all the monitors (pending suitable connections on said monitors too), every brand is different so you really need to check the manufacturer's website to see what sockets they have.
Thats a link to the model on the homesite, but even there it seems there are numerous flavours of that model, so you'll need to be careful about checking the model codes against the specs when buying.
ATI Eyefinity Requirements
Windows Vista and Windows 7 operating system (Eyefinity is not supported in Windows XP)
A graphics card with at least one native DisplayPort output
Display with native DisplayPort
Use of an certified active DisplayPort adapter is required to convert the DisplayPort output on the graphics card to an output compatible to the display when more than two displays are used in a multi-display configuration (available for purchase separately)
I was reading a manual for that series and it says this:
"Your ATI Radeon HD 5750/5770 graphics card provides multi-display functionality
through its various display connections. The graphics card can output to a
maximum of three displays using the following set of connections:
• Two DVI-I Dual Link connections and one DisplayPort connection."
so that's sounding to me 2x dvi and a displayport at once for 3 monitors is fine.