Before we learn how to properly tie a taekwondo belt, you should probably have a little background information. Tae kwon do originated in South Korea, where it is a national sport, much like football in the USA. The different belt colors symbolize different stages in development.
(Note: I am only listing the belt stages as I was taught, and of those, only the more significant stages)
The white belt is the [first] belt, and symbolizes purity. The white belt is the most important stage; it is where you begin to see what will come, and where you begin to gain flickering insight into who you are becoming.
The [second] belt is often yellow, this represents the earth; as your roots have begun to grow. Some people (like myself) skip this belt, and jump straight to orange belt, which symbolizes the suns rays which strengthen the seedling.
The [third] belt is green. This represents the plants growth, which had been enhanced by the earth and sun. Also, just as plants must weather their storms, this is the stage during which you begin sparring, using kicks only.
The [Sixth] belt is blue with a black stripe, often affectionately referred to as a "bruise" belt. This is the stage in which your forms will become noticeably harder, and this is when you are allowed to begin using your hands during sparring (hence "bruise" belt).
The [ninth] belt is black, with a varying number of yellow stripes embroidered at one end with your name, the other end generally has the name of your school/association. Oftentimes the most anticipated belt, a black belt symbolizes maturity. I am a first dan. This simply means that I have achieved one golden stripe at the end of my belt.
Step 1: How to Tie a Tae Kwon Do Belt: White Through Red W/ a Black Stripe
First, you must be wearing your uniform. For all ranks lower than that of black belt, that generally means the white pants and jacket you purchase [from your instructor] as a white belt. (My instructor allows us to wear the bottom half of our uniform and a solid colored T-shirt.) When you are properly dressed take your belt, and find the midpoint. The midpoint of your belt should be relatively centered in the line of your torso, at or slightly below your belly button. With the belt centered, wrap both ends around yourself, and pull until it isn't too tight, but will stay up. Cross the right side over the left, and tuck the end of the right under the left, and tighten. Tie another knot on top of this one and you should end up with a triangular shape in the center of your tied belt.
Step 2: How to Tie a Tae Kwon Do Belt: the Black Belt
When you first become a black belt, a first dan, you accept the responsibility of being a senior student. As a second dan, you should be able to take over a class and continue teaching where the instructor left off. As a third dan, you are allowed to become a co-teacher, or start your own classes.
To tie your black belt, take the end with the name of your school/association and hold it to your left side. Take the right end, the end with your name and rank of black belt, and wrap it twice around you. After this, tuck the end under BOTH layers. From here, fold the right end over the left, and tie a knot. From here tie one more knot, and you should be able to see both the name of your school/association, and your name/rank of black belt.
Congratulations, you now know how to tie your tae kwon do belt!