Installing a New PCI or AGP Card
Terminology
AGP: Accelerated Graphics Port. Usually used for graphics cards, high-end ones at that. It comes in 1x, 2x, 4x and 8x speeds. It's usually a dark brown, shorter slot on the back of the motherboard.
PCI: Peripheral Component Interconnect. This is the standard bus for most computer cards, like modems, LAN cards, lower-end video cards, TV-cards, and other expansion devices. It is longer and ivory or white in its slots, and there are usually 3-5 on a standard motherboard. PCI-Express has just come out and is the fastest bus to date.
Installing a New Card
If you're installing a card into an empty slot, follow these instructions:
Disconnect the power, use a static wrist strap and open your case.
Get rid of the metal slot cover on the back of the PC. In newer cases, this will probably just need to be unscrewed and removed. In older cases, it's actually attached to the case by slivers of metal. In this circumstance, you'll have to pop it out, and probably bend the heck out of the metal slot to actually get it out of the case. Using the screwdriver is the easiest way, but be careful not to cut yourself on the metal, shock yourself on the motherboard, or break any components applying too much force to the screwdriver.
Once the metal cover is out of the way, make sure you are installing into the right slot one more time. Gently slide the card down into the slot, being careful not to pinch any wires or scratch any contact points. Slide the card all the way down into the slot. If it won't fit, don't force it unless slightly more pressure will push it in. If the metal tab at the bottom of the card is holding it up, then bend it slightly out of the way.
Now that the card is in the slot, replace the screw and secure the card into its new location. Connect any cables necessary to the card, such as extra power or a LAN wake-up option. Power your PC on, but don't touch anything while it is powered. Make sure the new device works. If it does, install the drivers for it, reboot and double check it. If everything clears, disconnect the power, close the case up and you're ready to go. If it craps out, refuses to work or has other issues, check the instructions. If it is a driver issue, then install the newest drivers. If you can't figure out what's wrong with it, you may have a faulty card. Contact the store or company for tech support.