This is how all the Saiyans turned Super Saiyan.
Goku was the first and he changed when Freeza blew up his bestfriend Krillin.
He Also turns Super Saiyan 2 and 3 with alot of hard training.
Gohan turned Super Saiyan when he is training in the hyperbolic time chamber.
He Turns Super Saiyan 2 when he see andriod 16 blown up by Cell.
Vegeta turns Super Saiyan when he is mad cause he can't be Goku.
Vegeta turns super saiyan 2 while training for Gokus Arrival from death.
Goten turns Super Saiyan when his mom kicks him.
Future Trunks turns Super Saiyan when Gohan is killed by the andriods.
He turns Super Saiyan2 in the HB when training with Vegeta.
Chibi Trunks turns super saiyan while training with his dad Vegeta.
Gotenks turns Super Saiyan 1 and 2 out of pure power.
He turns super saiyan 3 in the HB training for Buu.
Vegetto turns Super Saiyan out of pure power.
Gogeta Turns super saiyan when theres a crises between them and Janemba