Grandpa Son Gohan's training:

While Goku was growing up as a child, his Grandpa Son Gohan trained him martial arts. There was no style specified, but what is known it that Grandpa Son Gohan was trained by Muten Roshi. This is Goku's foundation for fighting.

Oorinji Temple training (Krillin's initial training):

Before Krillin trained under Muten Roshi, he used to practiced the Oorinji temple monk style. He trained there for 8 years. He left the temple because the monks there teased him about his size. Not much is know about how much training he had, but we can assume this is his foundation.

Muten Roshi's training:

Muten Roshi took Goku and Krillin under his wing, as such this training consisted of little martial arts and designed to increase strength. Some of the tasks that Krillin and Goku had to do was delivering milk on foot while wearing 20 kilo turtle shells, and plowing large farm fields with their bear hands. After the training, Goku and Krillin's strength nearly tripled. At some point and time, Muten Roshi also trained Yamucha.

Karin's "holy water" training:

The legend says that whoever drinks the holy water at Karin's tower, their strength will be doubled. But the trick behind the increase of strength is the effort and energy put into getting the holy water from Karin himself. The result is a training session with one of the fastest cat on planet earth. Mutenroshi trained under Karin when he was young. It took the great Mutenroshi 3 years, while it took Goku 3 days to get the holy water.

Tsurusennin's training:

At some point in the time line, Tein-shinhan and Chaosu are disciples of Tsurusennin (he is Muten-Roshi's primary rival and enemy). Although Tsurusennin and Muten Roshi trained with the same teacher (Mutaio-sama) in the past, their martial art style is vastly different from each others. This style of martial arts is Tein-shinhan and Chaosu's foundation.

Kami-sama's training?!?