A computer is a very simple machine put together with very complex parts. As a user, the complex part is an area not to be worried about.
If you take a look inside your computer, you will see only a few items that make the machine work. Lets start from the top.
Most people always ask about the Hard Drive first, cause this is were all your information is. The Hard Drive is nothing but a metal box with a couple disc's inside. Kind of like a couple CD's sitting on top of each other, but more complex. Take a look inside the Hard Drive-

                                                                        

As you can see, there's really not that much to them. But these simple parts put together just right will store a lot of data.

Hard Drives are mostly used for the main operating system itself, however more and more people are purchasing second Hard Drives to use to backup information. A smart thing to do if you run a business or have a lot of stuff you do not want to loose.

Another thing to look for when replacing your Hard Drive is what type of Hard Drive is it. There are 2 common types of Hard Drives in computers. IDE and SATA. IDE is an older style not commonly used in computers today. But there are still hundreds out there that have them. Here are the differences-
                                                               
                                                        This is a IDE style HD                                                 
                                                                            
sATA


Next lets talk about the Mother Board. The Motherboard is nothing but a circuit board designed just right. A complex piece to build, but for a user just a simple board.
Without the board, you have no computer. You need the board to connect everything to.

The problem with boards today, is there are so many different types. This is due to companies doing there's just a little different to sell a product for less. But now the competition is large, that most boards cost about the same no matter the type. There are a couple things to look for if you need to replace your board, and those are:

1- What is the socket type? The socket is were the CPU will go, and depending on the socket you have to use certain cpu's or processors. Here are a couple different sockets-

         Socket 370                                              Socket 478                                              Socket 775                                                 Socket 939
                                                                    

You can see just from these 4 pictures the difference in sockets, and these are just a few out of many. So before you run out and buy a new board, make sure you know what type you will need.
Now your asking, "why can I not see this?" This is because it is under the fan which sits on top of a metal or aluminum box which is held in place over the CPU to the board. "what?"

The CPU which sits inside the socket above gets to a very high temp and needs to be cooled. To do this they used an aluminum element which sits on top of the CPU, and a CPU fan on top of that.  Without this, your CPU would explode!

Don't believe me? watch this-



So, this video pretty much sums that up. This is also a good reason to keep your computer clean from dust. A little wont hurt, but I have seen some computers that had dust built up so bad, I had to take them apart just to clean them.

With the heating element, the style of the element is also something you need to keep in mind for your system. Again, different boards have different socket types and this will also affect the type of heating element you need.

The CPU fans are pretty basic as you have already seen. Its just a simple fan screwed to the heat element that pushes air down to help keep everything cooler.
A different form of cooling your system is liquid cooling. Liquid cooling is very nice for a couple reason: 1- Its so much quiter. 2- It maintains the system temp much better.
Liquid cooling is pretty much just like a cars radiator. The vehicle uses fluid to keep the engine cool. Here is a picture of a liquid cooled system-



Now lets talk about the Memory or RAM. Again there are a couple different types of memory, but pretty standard in most computers. The 2 most common types are DDR and DDR2. Of course now they have DDR3, and soon down the road someone will come out with DDR10. We always need more power.

You need to find out what type of memory your computer uses. And you also need to find out the max memory. If you put too much in, the computer will only use what it can, the rest is wasted. For example, my computer uses DDR3 and the max the board will accept is 8Gig. Of course I use all 8Gig, but if I were to put in say 10Gig of memory, the computer would only use the 8, and the remaining 2 is simply wasted. So in the end, I paid for 2 gigs of memory that I will not use.
As you can see from the pictures below, the different types of memory to vary. Check out the notches to see-

You can see the notches are in a different placement. So you simply cannot use the wrong type of memory in your computer because it will not fit!

Also remember that laptop memory is no different, just smaller.

The power supply is important, but most of them are the same. The biggest thing to consider is the pin configuration. Older style boards use a simple 20 pin connector. But the new style boards use whats called a 20+4 with an additional 4 pin plug that connects in a different location on the board. Here are some pictures-
               20 Pin                                                                            20+4 pin                                                                         The difference
                                                                               

Now keep in mind, the new style power supply units can be used on older boards, but the old style power supply units can not be used on new boards. There are adapters you can buy to make this work, but with the low price of a new box, why bother.

So, we have covered the Hard Drive, Motherboard, Memory and PSU. Whats left? How about the CD Drive?

A CD Drive is important to have, otherwise you would not be able to install additional software. There are only a few different types: CD Rom, CD Writer, DVD Rom, DVD Writer and the new Blu-Ray. All of these styles will work in a computer, its just a matter of what you want. I prefer to have 1 of each. A cd Writer, a DVD Writer and a Blu Ray burner. Why? for myself being able to burn dvd's or cd's for clients is important. Plus being able to burn that movie I liked onto a DVD is really nice, of course that also requires special software.

There is another part of the computer that is critical. Its a small piece that sits on the MotherBoard- the battery.
If the battery dies, your computer will not function. But this is a simple fix, just replace it.

You will also notice on the board that there are slots on the bottom left. These are known as card slots. The different styles are-

                  AGP                                                                                        PCI                                                                             PCI Express
                                                                                        

These slots are used extra cards. You can put in Audio cards, USB cards, Video Cards, TV Tuner Cards or pretty much anything. If your computer has its video card in one of these slots, than this means your computer does not have what is called imbedded video and needs that card for your monitor. Or if your like me and use a couple different monitors, you would put another video card in your machine to display 1 or 2 more LCD screens. Almost all new computers today you can do this without putting in another video card, but sometimes you just want more.
Having multiple displays can be handy, as in right now while I am typing this I also have a movie playing on another screen as well as another screen has google open for me to grab the pictures I am posting.

You might want to add another audio card for better sound. Again most computers today are setup to handle the 7.1 audio, but some are not. And if you want this, you have to purchase and add that card.

Everything in you computer can be replaced or fixed, although I have found out that simply replacing is cheaper than fixing.