Hi,
There is really not much to a graphics card replacement. Basically, uninstall previous graphics driver from the add remove programs in the control panel first while you still have your old card installed. Then power it off, remove the graphics card, put in the new one, boot up, then install new driver.
Graphics cards are made for several different expansion slots (different types of slots) so you need to know which ones you have on your motherboard. There are cards for AGP slots, PCI slots, and PCI express slots. Most of the newer cards out today are using PCI express slots of one form or another. Older boards may have an AGP slot (accellerated graphics port), and most system boards have a PCI slot which can support not only PCI graphics cards but other cards as well, such as audio cards. PCI express slots have a few different standards, like PCIe x16 or PCIe 2.0. The good thing is, you can buy a newer PCIe video card and it should be backwards compatible with older PCIe slots (it just wont run to its fullest potential because of bandwidth of older slot) but it will still work fine. Also, with some of the newer cards, you have to have extra power connectors (usually 6 pin connectors) coming from your power supply in order for them to work. So just be to check in the requirements of the card to see if it needs this extra power. Some cards will come with adapters for the power, so you could take a standard 4 pin power connector and still use it with the adapter for the card. One other thing to check as well for power is what the recommended wattage power supply the manufacturer recommends. It varies depending on the card you choose but its just something you should check before buying a new card.
Two good websites that you can check out different video cards to buy would be tigerdirect.com and also newegg.com. I have bought from both of them with no issues.