What makes someone go SS?
A saiyon's body is capable of reaching certain
levels of power. When this level gets higher than the body can suport,
usually from extreme rage or stress, it has to change. And I don't mean
stepping on their toe, I mean a major loss: Gokou first reached SS level
after witnessing the death of his best friend, Krillin; Vegeta for losing
his son.
SS2 is like going SS when SS, and requires even more anger. Gohan is the first to reach this level, making him the only one who could defeat Cell. SS2 is characterized by more and spiker hair, and a purple lightning eminating from the body. Going to this mode brings about some super-hefty fireballs, and some real furious battles.
SS3, unlike the first two levels, seems to be a matter of practice, not anger. As far as I know, only three have ever made it to SS3: Gotenks, Gokou, and Gogeta. Gotenks was the first (and the youngest) to reach this level of power. Also, the saiyon's hair becomes a huge mane, stretching 5 or 6 feet down their back.
Oozaro, when a Saiyon with their tail sees the Moon, they turn into a huge Monkey. Gold Oozaro is when a Saiyon turns in Oozaro form by looking at the Earth and not the Moon.
And finally there is the Ultimate Saiyon, SS4. This is only possible when reverting back from Golden Oozaro form. Gokou seems to have near god like power when in this level, and easily took out Vegeta in it. Unlike all previous forms, SS4 does not include blond hair, but black. Much of the body is covered with a kind of fur, and the hair gets real bushy. Only three have ever made it to SS4: Gokou, Vegeta, and Gogeta.