it's the card your monitor is connected to with a blue or white plug.
It will probably look like this:
http://www.newegg.com/Product/Produc...82E16814130063
Open up the case and check to make sure the cooling fan on the card is turning while the computer is on, try not to touch anything, and make sure you don't run the risk of a static shock on the computer.
When you look on the motherboard (biggest part of the computer), your video card is likely to be mounted in a blue (pci-express) or brown (agp) slot.
If you turn the computer off and try to turn the fan lightly with your finger, if it's working properly it should be very loose and easy to turn, if the fan itself actually shows some resistance and doesn't keep turning after you touch it, then it most likely means there's something wrong with it (it could mean the fan isn't able to turn fast enough to draw enough air onto the card's heat sink which will keep it cooled down)