When you need to replace your power supply it can be pretty scary to look inside and see all the wires that need to be connected. You will soon see how easy it is.
If your computer is a common brand such as HP, Dell, Compaq, Gateway, etc. and is fairly new (newer than 5 years or so) then the power supplies sold at most computer stores such as Best Buy (BestBuy.com) will work. If you have any doubt, then just ask the salesperson.
Unplug the power cord from the computer. Just turning off the power is not good enough because the power supply is still supplying power to some components. Lay the computer on its side and open the computer case. How this is done is dependent on the computer brand and model. It generally calls for removing screws from the back of the computer and removing one of the sides. Touch a metal part of the case to discharge static electricity that can damage the computer - or wear a static strap (can be purchased at computer stores)
Taking the masking tape, place the tape on each of the connection wires to the peripherals (such as hard drive, CD drive, DVD drive , etc.) and the motherboard. Mark which connection it is on the tape with the marking pen. You should have at least two connections to each peripheral - a data connection and a power connection. You can unplug them as you mark them. Also right down what you are disconnecting on your paper. Make sure the fan connections in the power supply are also marked and written down. The fans are what help keep the inside of the computer cool.
After you mark all the connections and they are unplugged, remove the screws that are holding the power supply into the computer and remove the power supply. Following the instructions that came with the new power supply, install the power supply into the computer. It may be slightly different than the one you removed so it is important to follow the instructions.
Using the old power supply as a guide, connect the power supply cables to all the peripherals, the mother board, and make sure the fans are connected. The plugs only fit in one direction so make sure they are correct and make sure they are tight / snap in. Mark off on your paper the connections as you make them. This will make sure you get everything connected. There will likely be many connectors not connected and that is perfectly normal.
After you install the power supply and you are sure everything is connected and before you place the cover on the computer, set the computer right side up and connect the power cord. Power the computer up and make sure the fans and all the peripherals are working. If something is not working, power the computer off and check the connections that failed. Retest until everything is working. Power off the computer, place the cover back on, then power up.