In this section, it will show the process of how a Saiyan-Jin is transformed to a Super Saiyan-Jin 3.  By showing the advantages and the disadvantages.  It also has some interesting facts on a certain character in DragonBall.  The high quality pictures might take a while to load.  Enjoy.
 

Saiyan-Jin
In the very early stage of a pure-blooded Saiyan-Jin, they all have black hair and they look just like ordinary people, except they have a tail at their rear end (like a money).  They gain their power level by training, fighting and improving.  The maximum power level can be gained by an exceptionly powerful Saiyan-Jin is around 20,000 or 30,000.  However, another way is to gain power by looking at a full moon (Ozuro Mode).  By looking at a full moon will transform them into a giant monsterous ape, which their power level is increased 10 times.

Advantage:

• When a Sayian-Jin is turned into an ape (Ozuro Mode), they gain great stength.

• If the moon is suddenly covered up by dark cloud or obstructed by a certain object, the Saiyan-Jin ape is instantly instantly transformed back to a normal Saiyan-Jin

• Trunks/Future Trunks is the only Saiyan-Jin who hasn't got black hair.  This is because he is mixed.
• In the very first battle between Gokou and Prince Vegeta, Gokou got his ass kicked by Vegeta when Vegeta is turned into an ape.
• Gokou's tail was removed in this very early childhood life by his master.  The master was afraid that Gokou might transform into a ape during night time.
• Gokou was born to be a much inferior Saiyan-Jin, with a power level of only 2.
• A Saiyan-Jin cannot turn into an ape if he/she hasn't got a tail.  The tail is where the energy is collected to transform into a huge ape.
• A Saiyan-Jin cannot go to SSJ or further if he/she has a tail.

Advantage:

• It increase the overall power.

• None

• Gokou was the first Earth-raised Saiyan-Jin to become a Super Saiyan-Jin, and maybe the first Saiyan-Jin other than Brolly (The ancient legenday Saiyan-Jin).  Vegeta got jealous seeing Gokou as Super Saiyan-Jin, therefore he quickly went back to martial art training which made him the second Saiyan-Jin to turn into a Super Saiyan-Jin.
• Goten is the first ever Saiyan-Jin who has the natural ability to turn into a Super Saiyan-Jin, without pushing himself to the limit.  Gohan found out this ability while he was training with Goten, while Gohan was explaining to Goten that Goten couldn't possible become a SSJ without pushing himself, then all of a sudden Goten just turned into a SSJ too.  Gohan was very suprised.
• Gohan turned into a Super Saiyan by training with his father Gokou during the battle with Cell.
• Gohan's death by Androides 18 and 16 triggered young Trunks' anger and the desire for revenge, hence transformed Trunks into Super Saiyan.

Advantage:

• As a SSJ 2, they have the abilty to adjust their strength/speed/agility.  More experienced fighters such as Vegeta and Gokou, they know how to balance up to make them well adjusted.  If successful, it can also result in increasing more strength/speed/agility.

• If one part of the power go up the other two have to go down.  For example, if a Saiyan-Jin chooses to have more strength, he/she has to sacrifice speed and agailty.  Simple as that.

• Vegeta was the first to be successful in adjusting his strength/speed/agility.  He firstly transformed himself into SSJ 2 form, and adjusted his strength/speed/agility while he underwent martial art training.  This sort of training had given Vegeta an extra boost in every part of his battle.  The results was clear, he had no trouble beating up Cell and got him packing to get more training.  This transformation by Vegeta was well superior, and by honoring his own success, he named this transformation as Super Vegeta.
• Future Trunks was also quite successful in building up his strength/speed/agility.  However, he concentrated too much on his power and left out the importance of speed and agility.  While fighting cell, he wanted to show off his training success and increased his power by a few factors.  True, his power was immensely great, but he didn't realise his speed and agility was letting him down.  Cell then told him that his transformation of increasing strength and decreasing speed was the wrong transformation and that will only get him killed at the end.
• Future Trunks went to Saiyan-Jin 2 by Gohan's death.

Advantage:

• The SSJ 3 has much greater strength/speed/agility.  Which it makes the Saiyan-Jin as a true complete fighter.

• Since a SSJ 3 is much more powerful, it uses up more strength too.  A SSJ 3 fighter can fight for a while, but he/she gets tired very quickly too.  It is know that resting will not build up strength, it will lose them.

• Gokou is the only Saiyan-Jin to get to this stage, apart from Brolly (I guess Brolly has the ability too).
• Gotenks is the first combined Saiyan-Jin to get to this stage.

I don't know too much about SSJ 4.  I know it comes out in the GT series, but I need more info on it.  If anyone knows much about SSJ 4, please email me.