Goku is a saiyan born on the planet Vegeta and was sent to Earth due to the planet being in grave danger, Frieza had decided that the saiyans were becoming too strong for his liking, and with the Super Saiyan legend lingering around, he wasn't taking any chances. Frieza blew up the planet along with Goku's father, Bardock, who fought against Frieza's soldiers in a bid to save the planet.
A while later, Goku's pod landed on Earth in the middle of nowhere. Being a baby, his power level was a pitiful:2, but soon after a kind old man named Gohan found him and raised him as his own, Goku's power and kindness rose.
The Hunt For The Dragon Balls
This adventure plunged Goku and his new found friend Bulma, into perilous danger while searching for the seven starred orbs known as the Dragon Balls. Whilst meeting many new friends and foes along the way.
The Red Ribbon Army Saga
This point in Goku's adventures tells the story of the fierce and cold-blooded Red Ribbon Army. The Red Ribbon Army are looking for the dragon balls in a bid to use them for world domination.
The King Piccolo Saga:
This story tells the story of the time where the Demon King Piccolo, took over the world, made crime legal, killed some of Goku's friends and nearly crippled Goku. Using all of his strength, Goku manages to impale Piccolo with his own body. As a last resort, Piccolo spits out an egg that with hatch and become, Piccolo Jr. A few years later, Jr and Goku fight at the World Martial Arts Tournament, Goku is rendered near quadropalegic by Piccolo but Piccolo eventually flees after Goku's display of power and sheer willingness to fight.
The Saiyan Saga:
This point in time is about saiyans. One Saiyan lands on Earth and reveals to Goku his Saiyan biology. Goku and Piccolo then fight this Saiyan called Raditz, who is also Goku's brother, this fight pushes both Goku and Piccolo to their limits and it takes the sacrifice of Goku to beat Raditz. After he is defeated, Raditz reveals that 2 more saiyans are coming in one year from then and that they are both more powerful than he is. After one year of training, the Z Fighters are greeted by the Saiyans via a bloody massacre of everyone but Krillin and Gohan. Goku then arrives after being revived and trained by King Kai. He easily defeats the first saiyan named Nappa, then the saiyan named Vegeta steps up to fight Goku. It was a hard fought battle but eventually Goku is victorious and Vegeta escapes barely alive.
Note that this article is NOT finished yet, there is still a lot more ground to cover on Goku.