PCI Express® based PC is required with one X16 lane graphics slot available on the motherboard
400 Watt or greater power supply recommended (500 Watt for AMD CrossFireX™ technology in dual mode) http://www.amd.com/us/products/desktop/graphics/amd-radeon-hd-6000/hd-6570/pages/amd-radeon-hd-6570-overview.aspx#3
1 x PCI Express x16 slot, running at x16http://www.gigabyte.com/products/product-page.aspx?pid=3262#sp
Should be good as far as running it.
If you plan to upgrade more in the future, you may want to see how much 12 volt current(Amps) for power supply has, but with your current cpu and that card, almost any power supply will run it.