Do you need an explanation of the story of Dragonball GT?
Goku is training with Uub win Kami's lookout, 10 years after the end of Dragonball Z. They had just completed their training and were fighting. Emperor Pilaf and his two minions (now all old fossils) break into Kami's Lookout unnoticed (with large mecha suits). They are looking for the Dragonballs again. They finally find what they think are the Dragonballs, but they are actually the evil Black Star Dragonballs, which were created when Kami released all the evil from his body.
Pilaf doesn't know this. He thinks Dragonballs are Dragonballs. So he takes them outside and calls the eternal dragon. Meanwhile, Goku finishes his fight and sends away Uub. He notices the Dragon being summoned and goes outside to investigate. He sees his old nemesis, who realizes that it's Goku, the kid who bothered him so many years ago. Pilaf orders his minions to kill him. They fire missiles from their mechs at him, but he easily disposes of them. Pilaf mutters under his breath that he wishes Goku was the way he was before, so he could defeat him.
The dragon hears this wish and grants it. He turns Goku back into a kid again, like in Dragonball. But Goku doesn't even care that he was turned into a kid. The Dragonballs get scattered not across the planet, but across the entire universe. You find out later that the Black Star Dragonballs have a side effect. After a wish has been made, if the Black Star Dragonballs aren't returned back to the planet where the wish was made within one year, the planet will be destroyed.
So Goku, Pan, and Trunks search the universe for the Black Star Dragonballs, and that's how the whole series begins. During the series, Goku fights Bebi, who possess Vegeta, goes SSJ4 (when he does so, he turns into an adult), fights Super 17, and fights the seven evil dragons spawned from the seven broken dragonballs (which broke because of all the evil wishes that have been made with them).