Although it initially wasn't very common at all, the ability to fly eventually became commonplace in the Dragon Ball franchise. While it only really became a thing toward the latter part of the original series, by the time of Dragon Ball Z, literally everyone knew how to take to the skies. However, for as common as the power became, many still wonder how franchise hero Goku came to learn it.
Goku first uses a weaker version of flight toward the end of Dragon Ball, but by the introduction of his son Gohan, he's completely mastered the ability. This makes his exact education in the skill highly contentious among fans, but there's a pretty good exploration for how he came to first really use it.
Flight in Dragon Ball
The power for seemingly normal humans (and humanoids like Goku) to fly and levitate in the air was introduced with Tien, Chiaotzu and the Crane School, though the cat Puar had previously shown the same ability. This Crane School version of flight is referred to as "Sky Dancing," and the users usually don't just take off into the air as shown later in the series. Instead, they would more so "levitate" above the ground, although the ability was still useful. Even in this rudimentary form of the skill, the same concept applied to its more advanced version: an individual uses their ki energy to power their levitation and flight, with those with more control of their ki being able to do this nearly effortlessly.
Goku could apparently fly by rotating his tail as a child, but this ability was quickly lost once his tail was cut off. Before learning how to fly on his own power, Goku got around via the Flying Nimbus, a magical flying cloud. This mode of transportation is mainly used in Dragon Ball, since by the time of the sequel series, Goku and pretty much everyone else can fly on their own. How exactly Goku got this ability is never shown or stated outright, however, making many question how and why Goku ditched the Nimbus. Goku's talent for learning by observation and his training with a wizened Namekian might be the explanations for this newfound flight.
How Did Goku Learn to Fly?
As an adept martial artist and a master of drawing upon his own power and ki, it's entirely possible that Goku's flight powers got jumpstarted by fighting Tien. After seeing the Crane School student use his Sky Dancing technique, gears likely started spinning in Goku's head to teach his body to do the same. Likewise, by the end of the original Dragon Ball, Goku uses true flight against the son of Piccolo at the World Martial Arts Tournament. This is after he's become a young adult, having trained with Kami for several years and become much more powerful. By the time of Dragon Ball Z, Goku has completely mastered this power, likely due to his having trained quite a bit by the time of his son Gohan's birth and early childhood.
Goku's best friend Krillin is also established as having somehow learned to fly around this time, with Yamcha, another regular human, learning the power after training with Kami as well. It would seem that Kami's training helps to make ki manipulation easier for fighters, giving them the power to fly, among other things. It's thanks to this training that the franchise's main character was able to master flight and end the original Dragon Ball on a literal high note.
