The legend of SSJ is that everyone 1000 yrs there is one saiyan that emerges as a Super Saiyan (even though in the series almost all the saiyans go at least Super Saiyan. A saiyan can acheive Super Saiyan by getting extremly angry because they get "backed into a corner" where the only way to get through is to release their anger, or when they lose something dear to them such as when Frieza had killed Krillin and because Goku and Krillin where such good friends that Goku could not take the lose and erupted with tremendous anger towards Freiza, not caring how strong the monster was and completly destroyed him. The legendary saiyan that was thought to have had killed himself had lived. He had not been killed by his own power because he did have control over it. Broli was the original Super Saiyans name and he had a deep hatred of Goku, but he is eventually defeated by Goku and his sons three times.

Super Saiyan (form 1)

First achieved by Goku in Frieza saga, in this stage the saiyans hair turns gold , his eyes turn green, and he becomes more muscular, and has a great amount of speed and strength, it can be acheived by any saiyan with wither a pure good/evil heart, all the saiyans in DBZ,DBGT (accept for Nappa and Raditz) went SSJ but not all went past Super Saiyan accept through fusion-(Goten+Trunks=Gotenks)

Ultra Super Saiyan

This stage is between SSJ1 and SSJ2 where the saiyan gets more muscular, but because of this he slows down tremendously, Trunks is the first to find this out in the Cell Saga where he fights Cell,but is to slow to hit him, it also reached by Vegeta when he is showing of his power, but Vegeta knew of the fact that he had slowed down tremendously so he did not go into Ultra Super Saiyan

Super Saiyan (form 2)

This stage is first reached by Gohan in Cell Saga, in this stage the saiyan grows more golden hair, he also becomes more muscular and at the same time gains speed. As Super Saiyan 2 it seems that the super saiyan has electricity surging through him, and as seen when Gohan fights Cell that even when they are crippled a Super Saiyan 2 has still tremendous power.

Super Saiyan (form 3)

This stage is first reached by Goku in Buu Saga. In this stage the saiyans hair grows down to this knees, he loses his eye brows, and gains tremendous speed and strength. I don't know much about this stage other then that this is the last stage that a Super Saiyan has golden hair before he turns Oozaru, and then Super Saiyan 4.

Super Saiyan (form 4)

First reached by Goku in the Bebi Saga, then by Vegeta (after Bulma created the Brute ray) This stage can be reached after the saiyan has control over Golden Oozaru form, the saiyan grows a tail, his hair turns black, and he has rings around his eyes, and his eyes are also black, he also grows red fur on his body, and is very powerful with muscular enhancement and tremendous speed, this SSJ form is the greatest form of them all and so far if the series doesn't continue then the greatest SSJ form to be acheived.