Look in the computer case, the video card should be in a brown slot that is set slightly further back from the back of the computer than the white PCI slots.
Disconnect the power and make sure you ground yourself out.
Disconnect the monitor cable, remove the retaining screw, flip the retainer clip at the back if you've got one, and gently remove the existing video card.
Take the Radeon out of the packaging and gently, but firmly push the card into the AGP slot until it won't go any further, gently rock the card from front to back if it won't go.
Reattach the retaining clip and screw, and reconnect the monitor cable.
Reconnect the power and start the computer. When Windows starts, remove the old drivers and install the new drivers, unless of course you're going from one ATI to another.