Would be nice to know WHAT computer we're 'talking' about here!
Does it have Integrated graphics, or a graphics card? If it has a graphics card, it will be in a sideways slot, on the back of the computer, where the monitor itself plugs in.
Look at this example:
http://www.newegg.com/Product/ShowImage.aspx?CurImage=83-229-051-11.jpg&Image=83-229-051-02.jpg%2c83-229-051-03.jpg%2c83-229-051-04.jpg%2c83-229-051-05.jpg%2c83-229-051-06.jpg%2c83-229-051-07.jpg%2c83-229-051-08.jpg%2c83-229-051-09.jpg%2c83-229-051-10.jpg%2c83-229-051-11.jpg%2c83-229-051-12.jpg%2c83-229-051-13.jpg%2c83-229-051-14.jpg%2c83-229-051-15.jpg%2c83-229-051-21.jpg%2c83-229-051-16.jpg%2c83-229-051-17.jpg%2c83-229-051-18.jpg%2c83-229-051-19.jpg%2c83-229-051-20.jpg&S7ImageFlag=0&WaterMark=1&Item=N82E16883229051&Depa=3&Description=CyberpowerPC%20Gamer%20Infinity%20SLI%209311%20Core%202%20Quad%20Q6600(2.40GHz)%204GB%20DDR2%20Dual%20NVIDIA%20GeForce%209800%20GT
See the ventilation holes down on the lower right, in a column shape?
To the left of them are the slots I'm referring to. These are expansion card slots. If the monitor is plugged into a card that is in one of these slots, you have a dedicated graphics card.
Now look at the round set of ventilation holes. To the left of them is the I/O Shield area. (Input/Output devices plug in here) If the monitor is plugged into a 15 hole plug,(VGA. Has 5 holes, in three rows, staggered.), in this area, you have Integrated graphics.
There will be NO graphics card to replace. You will just insert your graphics card, in the appropriate slot.
Now since again, I don't know what computer this is, I can't tell you if you have a PCI slot, AGP slot, or PCI-Express x16 slot for a graphics card.
This is an example of a motherboard that has an AGP slot for graphics. (AGP=Accelerated Graphics Port)
http://en.wikipedia.org/wiki/Image:ASRock_K7VT4A_Pro_Mainboard_Labeled_English.png
Look towards the top right. See where it says 'AGP Slot', and points to the black slot?
This one has an AGP slot also.
http://en.wikipedia.org/wiki/Image:Cusl2c.png
It is the brownish/black slot, to the left of the 6 PCI white slots.
If you just have PCI slots for graphics, you'll just see White PCI slots like these. (There will probably be expansion cards in these slots. If any one of them is open, with nothing in it, you can use it for a graphics card. Doesn't matter which ONE. As long as there's nothing in it, you're good to go!)
1.PCI: http://en.wikipedia.org/wiki/Peripheral_Component_Interconnect
2.AGP: http://en.wikipedia.org/wiki/AGP
3.PCI-Express: http://en.wikipedia.org/wiki/PCI-Express
Now we come to the newest form of graphics slot. The PCI-Express x16 slot. The above gives you info on it. The link below shows you what a PCI-Express x16 slot looks like on a motherboard.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3761586&Sku=E145-2038
Scroll down this page, and as you do keep your eye on the green slots. These are PCI-Express x16 slots. This particular motherboard has two. They are green. Not all PCI-E x16 slots are green.
This is from ATT.Yahoo Tech.
http://tech.yahoo.com/gd/upgrading-your-pc-add-a-new-graphics-card/166360
1.First thing is to unplug the computer from the AC source of electricity.
2.Next unplug all cables, and familiarize yourself with where they go before you unplug them. ESPECIALLY the speaker plugs. Sometimes the colors are close to each other,(PInkish, light orange, etc.), and when it comes time to plug them back in, you may be at a loss. Still have the Setup Diagram? Good! But if Mom has to dig it out, she may lose faith with you. Be a pro! Write it down if you have to!
3.If you don't do anything ELSE, DO THIS!
Work on a table. Wash your hands with warm, soapy water, dry them well. You may be the cleanest person in the world, but your body still carries static. Static is a silent 'killer' of those delicate computer parts inside. Open the case. (If I knew what computer!) TOUCH the metal frame of the computer case to de-static your body. Touch it before you reach inside. Touch it before you take that graphics card out of it's anti-static bag. Touch it if you get up, walk away, then return.
If the computer has a graphics card already installed, it will be held in by a Philips screw on the inside. This will be towards the outside of the computer case, in the metal frame. OR, there may be a metal panel on the outside of the case, where you remove a Philips screw,or a Thumb screw. The panel swings to the outside. Remove the graphics card by holding onto the corners, and rock it gently side to side, while pulling up. It will be pretty tight. Putting one back in, can be fun sometimes. The metal tab, on the metal face of the graphics card, has to go in-between the metal frame, and the motherboard. WHILE you are lining up the gold plated contact pins on the bottom of the card, in the graphics slot. AGP, and PCI-Express x16 slots have a lock on the slot.
Edit: This lock is pushed in, not pulled out! When you get the graphics card, follow the Quick Install Instructions. I take the CD that comes with the card, and with the computer on and running install the contents of the graphics card. I then power the computer down normally, and install the graphics card.
A lot of times if you install the graphics card first, Windows tries to use one of it's generic drivers. You need THE drivers that comes on the CD.