In the year Trunks is born, Goku contracts a deadly heart virus and dies. Everyone deals with the grief in their own way, but then two Androids showed up and began to wreak havoc on the world. Krillin, Tien, Yamcha, Chaouzu, Piccolo, Gohan, and Vegeta go off to fight them, but they are all killed with the exception of Gohan. Barely escaping that battle, he trains hard and becomes a Super Saiyajin.
13 years later
By now the Androids have managed to wipe out much of the world. Gohan, who is busy trainig Trunks to become a Super Saiyajin, has fought them many times and failed. So he and Trunks train to get stronger. Trunks tries many times to go SSJ, and while he almost makes it, he never fully succeeds. Then the Androids(oh by the by, their Androids 17 and 18) show up, and the two go off to fight them. They get badly beaten and Gohan gives Trunks the last Senzu bean. After recovering some, Gohan resumes his training of Trunks. Once again, the Androids show up. Gohan prepares to go after them alone, but Trunks insists that he go, too. Gohan protests at first, but then changes his mind and agrees. Right before Trunks is about to take off, Gohan hits him in the neck, knocking him unconscious. Gohan then goes off alone and ends up getting killed. Later, Trunks awakens and finds Gohan dead, which angers and saddens him, causing him to go Super Saiyajin. (And while many people make fun of the fact that he yells GOHAN-SAN!!! over and over, I found it very sad. I cried =P)
3 years later
Bulma has built a time machine, believing there is nothing else left to do but send Trunks in the past to when Son was alive(And no, i didn't forget the word Goku). But Trunks says he believes he is strong enough to fight the Androids and destroy them now, since he is a Super Saiyajin(shades of Vegeta ^_^). Even though Bulma protests, he goes off and fights and nearly gets killed. After Bulma finds him and he recovers, he realizes he is not strong enough, and goes back in the past to when Son was alive....