Most Saiyan who evolved into a Super Sayajin were only able to do so after a great amount of effort and trouble: Goku(Goku, Vegeta, Gohan, etc.) who evolved into Super Saiyan had trouble fulfilling one of the requirements to evolve: Their rage or other emotions had to be extreme.
ButHowever, there are two exceptions: Goten and Trunks (not the Trunks from the future). How did they achieve it? They hadn't seen or done anything that could drive them to such a level of rage and etc./intense emotion to allow them to turn into Super SayajinSaiyan.