This is the first stage of Super Saiyan. You reach this stage by having a loved one killed or having a need so great that becoming this is the only way to fulfill it. Your hair stands up and turns a golden yellow. You also have a golden aura around your body. It is a huge power up from normal saiyan. The first saiyan to reach it was Brolly(The legendary super saiyan) but Goku is credited becoming the first super saiyan in DragonballZ.
Super Saiyan 2
You become super saiyan 2 by becoming so enraged that you dont care about anything but to destroy your enemy. When you reach this point you just explode with rage. Your hair turns more of a yellow color and is more pointed toward the center. Gohan is credited for being the first saiyan to reach this point.This is how he destroyed Cell in the cell Saga. It is alot stronger than level 1 but in later episodes this is not so. In some occasions some people skip this stage to go on directly to level 3.(ex: Gotenks and Vegetto)
Super Saiyan 3
This level is far superior to the other 2. In this stage you have a massive increase in power, strength, and speed. This level uses up a large amount of energy and puts a great strain on your body so the character can only sustain it for a short amount of time. Your hair grows to the length of your knees but it stays the same color. I belive it was Gotenks who first reached this level. I'll Check on that later.
Super Saiyan 4
This is the stage that most people dispute. Some people say that this really isn't another stage of super saiyan because it doesn't include the glowing blonde hair found in the previous levels. I believe that it is the ultimate stage of that saiyan, super or not. In this level your body is covered in thick red fur. Your hair is back to the normal length and color. This stage has power that is unimaginable. People who have reached this level- Goku and Vegeta.
Super Saiyan 5
I have heard different views about this stage. Some people say it exists and others say otherwise. If you have and information on this level please email me some information on it.