Ok! Here is the stages of Vegeta and how he got there!

No.2 Super Saiyan Vegeta
How? Let Veg explain- Well, I just didn't care anymore if kakarotte was stronger than me, didn't care! That's when it happened..Vegeta was training in space when a group of rocks came down at him, normally it would've been easier for Veg to blast them all away, but after training in 300 gravity he couldn't. He was badly wounded and them he turned super saiyan. Click to see the pic!
Changes: He gets yellow hair. He is really strong to!

No.3 super saiyan 2 Vegeta
How? Vegeta turned super saiyan 2 when Babidi took over his mind. He gave Vegeta a lot of strength. If you are confused click here to read about Veg being Majin (when Badidi took over his mind). This isn't a very good picture, but I'll get another one soon.
Changes: He got more hair, well a bit, and way more stronger.

No.4 Super Saiyan 4 Veg
Vegeta was super saiyan 2 and about to fight this guy that ssj4 Goku was fighting. Then Bulma was saying how all saiyans have the same blue waves or something and said that she could make Vegeta turn Super Saiyan 4! So she zapped him with a ray and he turned ssj4!
Changes: As  you can see he has fur a tail and black long hair. New clothes to! And of course he is REALLY REALLY STRONG!