Dragon Ball Z opens with Goku gathering some fire wood (acually a whole tree). He then goes going to visit his old friends on Master Roshi's island. But soon Raditz arrives and tells Goku that he is a Saiyan from outer space, and that he is to rejoin the Saiyan forces and that Raditz is his older brother. Goku refuses to join Raditz, and Raditz kidnaps his son, Gohan. Piccolo decides to join forces with Goku temporarily to end this new menace because he has his own plans for conquering the planet.
The battle ensues with Raditz easily holding off the attacks by Goku and Piccolo. Piccolo's special beam cannon is strong enough to kill Raditz, but not fast enough to actually hit him. Goku finds his window of opportunity by remembering the weakness that daunted his childhood, all saiyans have a tail! He grabs Raditz's tail paralyzing him but Goku's trusting nature causes him to let Raditz go only to be double crossed and beaten horribly. Gohan's rage builds up and explodes into a fury of power as he head butts Raditz. In Raditz's weakened state Goku grabs Raditz making him unable to move. Piccolo uses his special beam cannon killing both Goku and Raditz.
After Goku's death, Kame, the guardian of the Earth, requests he be sent to King Kai's place for special training. The Earth's defenders find out that more Saiyans, much more powerful than Raditz, will be coming soon. Piccolo takes Gohan, after seeing his high power level, for special training for the upcoming fight. The other fighters, Tien, Yamcha, Krillin, and Choazu, Yajirobe, begin training in Kame's lookout for the Saiyans' arrival. Goku makes it to King Kai's after a couple misadventures on the Snake Way path and begins his training.
One Year after Goku's death the Saiyans arrive on Earth, looking for the dragon balls. The Earth's special forces arrive after Nappa destroys a small area of a city. Soon the media and the military arrive to watch over the monumental battle. Vegeta and Nappa, the two saiyans, decide to employ the help of their Saibamen, small green men who grow out of a seed planted in the ground in a couple minutes time. Piccolo, Gohan, Krillin, Yamcha, Tien, and Choazu decide to fight the Saibamen one at a time. Vegeta agrees to those terms and the tournament like battle ensues. Yamcha beats a Saibaman, but while his back is turned, it jumps from the ground and latches onto him. It self destructs, killing Yamcha in the process. Krillin gets really mad and fires off a blast that starts the end of the Saibamen. Once the team has beaten the Saibamen, the bigger of the two saiyans, Nappa, steps up to battle.
No one is even able to touch Nappa, who proves way to strong and fast for the outclassed humans. Chiaotzu grabs on to Nappa to pull Nappa into an alternate dimension (kill him), but Nappa is too strong and Chiaotzu ends up dead. Tien goes into a rage, and launches an attack against the giant alien. While distracted by Tien Piccolo and Krillin attack on Nappa's blindside knocking him out of his senses and plummeting toward the ground. Gohan panics and is unable to give the final attack that would have surely given and end to Nappa. Nappa is a little bruised after the fight but he is pretty unharmed. Tien, with his last ounce of strength launches an energy blast toward Nappa. Nappa dodges it (but just barely) and Tien dies after giving everything he had toward the energy blast against Nappa. Just as Nappa goes to fight against the remaining 3 fighters, Vegeta calls a time out to give Kakorot (Goku) time to arrive on the scene. The 3 hour time out expires and the fighting resumes. Nappa launches a blast at Gohan, and Piccolo jumps in front of the blast and takes the shot. Piccolo dies from Nappa's blast, but Gohan is spared. Nappa's assault continues against Gohan and Krillin. Goku arrives just before Nappa kills Gohan , saving him with his flying nimbus.
Goku makes sport of Nappa for a bit before eventually Vegeta, sick of his partner's incompetence, kills Nappa. That leaves Vegeta and Goku to battle it out. The fights runs to a stalemate before Vegeta pulls out his ace, a blast of energy meant to mimic the full moon. Vegeta goes into Oozaru, big monkey, form and starts to convincingly win the fight. Eventually the cowardly Yajirobe comes to the rescue cutting off Vegeta's tail. Goku blasts him with a kamehameha, sending him far far away. Yajirobe leaves before Vegeta can come back, and Goku tries to gather what little energy he has left for the rest of the fight.
After the battle ends and Vegeta retreats back to space, Goku, Krillin, and Gohan are rushed to the hospital. Krillin and Gohan are out in no time but Goku isn't so lucky. He's in a near body cast. Now that Piccolo has died that means Kame has died, due to their link. So Bulma decides to lead an expedition to Kame's home planet, Namek, to use their dragon balls to revive their fallen comrades. They acquire Kame's old ship and take off for the far away planet. They run into a couple obstacles along the way, a fake mockup of Namek with some malicious aliens, and a spaceship filled with refugees who think they are the bad guys. But they eventually arrive on the Namek. Goku gets out of the hospital when Yajirobe brings him a Sensu Bean to heal him. He gets a ship from Bulma's father, Dr. Brief, and heads toward Namek to help his friends.