Adding memory is pretty easy. First, what type of computer do you have? If it is an out of the box (ie: HP, Dell, IBM, etc) there should be a description of the type of memory that your computer uses in the manual.
There are 2 types of memory that are most common right now:
SDIMM and DDR. If you have a newer computer, there is a good chance that it is DDR memory. If you want to check how much memory you have, if you are running WinXP, you can right-click on the "My Computer" (either on your desktop or in the start menu) and select "Properties" (bottom pop-up menu option).
This will bring up a description of your computer. OS (including Service Pack Level), Processor Speed, and amount of physical memory (RAM).
It will probably be either 256 or 512 MB.
Also, before you are going to add memory, read your computer manual to see how much physical RAM your motherboard can hold. Should be part of the description. If you are at the peak, then you will need to get a new motherboard.
Once you have figured out the type of memory your mother board takes, and if you can add more, you gotta go buy it. It would be a good idea to open the computer and see how many slots you have as well. They are easy to find as they are long and skinny, and usually situated close to the processor.
As far as actually doing the physical work.. there are tabs at either end of the memory holder, you just have to pull one tab on either side away from the memory stick, and it will release the memory stick.
Putting the memory in, is just as easy. Open both tabs at either end, slide one side of the stick in (about a 45% angle), and then put the other side down. If you did everything right, the tabs will close and lock the memory in place.
Done like dinner.
edit: The reason you want to check to see how many slots you have and how much memory you have right now, and how much your motherboard can take. If you have 2 slots and they both are bing filled, and you have 256 total memory. That means you have 2x128MB memory sticks. If your computer can handle 512 or 1024MB of RAM, then you can buy 2x256MB or 2x512 or 1X1024MB sticks. Keep in mind, the larger the amount of memory on one stick, the more it will cost you.
You will have to take out the other memory..I am assuming you knew this though

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