Early in the dragon ball series when Goku is travelling with Bulma, who at that time is searching for the Dragonballs so she can wish for the perfect boyfriend, the pair meet old Master Roshi who is in possession one of the Dragonballs (the 2 star ball). They then don't meet again until Goku meets Chi-Chi and the Ox King and Goku and Chi Chi must go to Master Roshi's island for a fan to fan out the flames on the Ox King's castle.
It then turns out that Roshi no longer possesses the fan and goes personally and ends up destroying the castle with the first Kamehameha of the series (with many more to follow) It is after this that Roshi agrees to train Goku an offer Goku decides to take him up on once all the Dragonballs are found.
World Martial Arts Tournament Saga
Later after Pilaf is finished Goku decides to pay Roshi a visit for his training but before the training begins another Student shows up, Krillin. After a while Roshi agree's to train both the boys and thoughout the following months Roshi trains them up for the World Martial Arts Tournament.
The training consisted of delivering milk, swimming lengths in a lake with sharks, farm work and construction, all the while wearing a heavy turtle shell.
Once the tournament begins Roshi is nowhere to be found as he has secretly entered the tournament under the guise of Jackie Chun. He does this to ensure that his pupil's do not win the tournament and get big heads and stop training.
The first match Jackie Chun takes part in is against Yamcha who he defeats with ease. He then takes out Krillin in the next round. In the final round he is matched up against Goku who puts up an excellent fight against his master but in the end Roshi defeats him.