As mentioned by Tetras, post your power supply spec (it'll be on the side of the power supply somewhere) - wattage is the most important. Then assuming you have the headroom for an upgrade you could buy a molex splitter (to give you a spare power connection) and a molex to 6 pin pcie adapter as mentioned by srekal34 (or in case of no molex a SATA power splitter etc).
Then assuming the case will take the graphics card, just slot it in. You may have to change some settings in the BIOS if you're running on the iGPU to get a display from the new card.
You could take a pic of the internals and post here - someone will know the best route to take.