The setup
Before you start anything, make absolutely sure you have all the parts you need. There's nothing more annoying that having to search for some part while your computer sits in a room half-finished. Here is a rundown of what you'll need or want to have for your new setup.

CPU

First things first, you'll need the central processing unit, the 'brains' of your machine. Depending on the type you get, these chips can literally be worth their weight in gold. So handle them with extreme care! They usually come in a retail package with a heatsink/fan assembly included.

Motherboard
As the name would imply, this is the mother of all PC components. It is the pathway through which all computer parts communicate, and it is the device which controls the flow of traffic between the parts. It is, arguably, the most important part of your computer. For more information, check out our motherboard article.




RAM
Ram is the area of your computer that stores data that is currently being used, providing an interface that is nearly 1 million times faster than the ancient process of retrieving the needed data straight from the hard drive. This middle-man keeps the CPU properly fed with information for it to digest. Check out this article on RAM function for more info.


Hard Drives
These devices store your massive amounts of media files in a secure magnetized platter, ready to be transferred to the RAM when it's needed. Shoes wrote a good article on their function earlier, here.






Video Card
Because the CPU is designed to perform any task at a decent level, it can't perform any one task at a superb level. That's where video cards come into play. With their own processor and ram specifically dedicated to graphics, they can achieve hundreds of times the graphic capabilities of a CPU.





Power Supply
This is probably the most overlooked part of your computer. It provides a constant, steady flow of power to all your computer parts, which are quite sensitive to any sudden spikes in the flow. Once again, Shoes has a very thorough article on the subject here.






Case
Simple and straightforward. The enclosure that houses all of your computer parts, protecting them from dust and accidental damage.






Other Peripherals
These are any cards or other devices you're adding on to your system. Things like a CD/DVD-RW or a floppy drive, or even a sound card. Make sure you have these around, though you could really add them at any time. It is simply easier to add them all at once.