All Z Warriors train themselves. Every Z-Fighter has their own way of training which they like in their own way. Here is a list
of how some of them train:
Goku: Sparring, Weight Training, Repitive Exercises, Energy Blast Training
Gohan: Sparring, Fight Non-Stop, Turn His Emotions Into Power
Vegeta: Extreme Gravity Training, Defense Training
Chibi Trunks: Extreme Gravity Training
Piccolo: Intense Meditation, Fighting His Own Twin
Krillin: Sparring, Practice All Maneauveres Under Different Situations
Yamcha: Sparring, Practice All Maneauveres Under Different
Tien: Energy Blast Training, Weight Training
Chaustu: Mental Training, Physic Training
He trained most people during Dragon Ball and stopped afterwards since all of his pupils became stronger than him. He trained
Ox King, and Goku and Krilling who were two of his best students. Master Roshi is the one who gave Goku Nimbus and taught him
the awesome Kamehameha!
Kami calls for Z-Fighters when the Earth is in need of a strong warrior due to some evil. The first person he trained was in
Dragon Ball, Goku. He made him extremely powerful. Then in Dragon Ball Z, he trained Tien, Yamcha, Krillin, Chaustu, and
Yajirobe to help them prepare for The Saiyans (Nappa & Vegeta). Or to at least give Earth a fighting chance.
King Kai is possibly one of the greatest trainer. He first trained King Yamma. Then he trained Goku after he killed by Raditz,
and to prepare for the attack by Nappa & Vegeta. King Kai taught Goku the ancient art of Kaio-Ken. This taught him how to
increase all his senses giving him awesome powers. Kaio-Ken also let him do the elusive Spirit Bomb attack. Goku was the first
person ever to master Kaio-Ken. Even King Kai wasn't able to do this. Then after the Saiyan Battle, King Kai trained
Tien, Yamcha, Chaustu, and Piccolo who also became very powerful just like Goku.
Piccolo has only trained one other person in his life, and that was his first real friend, Gohan (Goku's First Son). During
the battle with Raditz, Gohan had exploded with anger and done some major damage to Raditz at only age 3! Realizing that Gohan
had incredible powers, Piccolo decided to train him in order to prepare for Nappa & Vegeta. He had a very touch time with
Gohan, but got him to become an awesome warrior.