all managed to work out what a Saiyan or even a super Saiyan is.  But just in case, here is the run down on the different levels a Saiyan can achieve in Dragonball.  

Oozaru- Any Saiyan with a tail can  turn Oozaru (giant monkey) by the light of a full moon.  Oozaru is strong and shoots energy blasts from his/her mouth).  It is only possible to reach this level if the Saiyan has a tail.  If the tail is removed or cut off the Saiyan can not transform.  If when the Saiyan is already Oozaru and the tail is cut off, the Saiyan will revert back to his original form.

Super saiya-jin (Super Saiyan, SSJ)- The Saiyan becomes much stronger and much more powerful.  their hair gets longer and turns gold.  Their eyes turn a piercing green and a golden ora surrounds them.  No tail is needed to transform into a Super Saiyan, but the Saiyan needs a certain amount of power to do so.  The transformation is usually triggered by anger.   A pure heart is needed to become a Super Saiyan (which is why Vegeta had so much trouble doing so-he finally did when he decided he'd  had enough of trying to be something he's not and that he doesn't care if Goku is stronger than him, or whether he lives or dies when he can't go SSJ).

Ultra Super Saiya Jin- The Saiyan becomes even more powerful then he/she already is.  The problem with Ultra SSJ is that the body becomes so pumped up the person becomes very slow, too slow to fight.  They still have long gold hair and green eyes.  This technique is demonstrated to Gohan by Goku in the 'room of time and space', but is warned of the speed disadvantage by his father.  Trunks uses this form against against Cell, but because of the extra mass he is too slow and can not beat Cell, even though he has the power to do so..

Super Saiya-Jin Level 2 (SSJ2)- Similar to SSJ, but much stronger and faster.  Hair gets longer again and is still gold as eyes are still green.

Super Saiya-jin Level 3 (SSJ3)- The super Saiyan looses his eyebrows (??? doesn't make any sense to me either).  Again, the Saiyan is much stronger and faster, and still has gold hair and green eyes.  This level is very rare and is not used much because it needs a lot of power and energy to sustain.

Golden Oozaru- Oozaru Saiya-jin monkey, stronger and gold fur.

Super Saiya-Jin Level 4 (SSJ4)- The final and the strongest and most powerful level.  The long gold hair and green eyes are lost.  The hair is much shorter and black.  The eyes are also dark and are outlined in red (looks like eyeliner gone wrong!!)  The back, arms, shoulders, tail and sides are covered with maroon fur.

This level was created by Ocean and was never in the original manga by Akira Toriyama.  He left before it was created and had NOTHING to do with it or the design of it.