You need to determine whether you have AGP (older) or PCI-E (newer) slot on your motherboard. You can tell just by looking at it. Search on google images, AGP and PCI-E, then look on your motherboard and determine which one you have.
I would clean any dust anyway, dust can brake all the electrical circuits on the motherboard as well as it can cause your computer to ovearheat.
Once you know which slot you have check your power supply for wattage and connections. Newer cards require 6 pin power connector. For any newer card I'd advise at least 450W - 500W PSU. Also, check if you have room to fit the graphics card inside your case.