@p in the beginning of the series, she was out looking for the Dragon Balls, because she found one and read about the legend of it granting a wish.

She is the daughter of the president/founder of Capsule Corp, which is the company that makes all the magic stuff that comes out from capsules, so she has a lot of robotic gadgets and vehicles and shit like that. She also created a radar that can locate dragon balls nearby, and she mets Goku because he has one that was left to him by his late grandpa (which we find out later was an old man who adopted Goku when the capsule containing him fell in the forest nearby).

Pre-DBZ Dragon Ball is actually pretty cool, and focus a lot more in the adventuring aspect. Then Toriyama found out that it was easier to just make an infinite series of "fighting tournaments" where people screamed at each other with increasingly ridiculous power levels, and here we are.