The components you need are:
Case
Power Supply
Motherboard
CPU
Memory (RAM)
Hard Drive
Optical Drive
Graphics Card
Operating System
As others have stated, it all starts with a budget and intended usage. You don't need a $1200 computer if you're only going to surf the web, read/write emails and watch videos. Similarly, a $400 computer is not going to play the latest games at anything but the lowest levels (if at all).
Which components you select are going to be based on both your budget and your intended usage. In most cases, it all starts with your CPU; in particular, which CPU best suits both your needs and your budget. From there, we can determine all the other components you need and can afford.
There is a sticky at the top of the forum which details the information we need to assist you further about asking for new build/upgrade advice. Please fill that out and we'll be in a much better place to assist you.
-Wolf sends