Heir to the Saotome Martial Arts School of Indiscriminate Grappling, he's been travelling all over Japan with his father, from one training ground to another. Finally, one of their trips leads them to China, to the training ground of Cursed Springs of Jyusenkyou. Unaware about the curse of the springs (Ranma's father couldn't read the guidebook when he planned the trip because it was in chinese), they both fall in the springs during their training.
Well, that's how they find out what the curse of the springs is about: it turns everybody who falls into it into the person or animal that first drowned in the referring spring when they get in contact with cold water. Hot water turns them back into their true forms.
So, since Ranma happened to fall into the Spring of Drowned Girl, he transformed into a girl. Ranma's father, however, fell into the Spring of Drowned Panda, so he transformed into a panda.

Ranma from birth was engaged to Akane Tendou, heir to the Tendou Martial Arts School of Indiscriminate Grappling. Their fathers, old friends since the time they both studied martial arts in the School of Indiscriminate Grappling, agreed to that. However, neither Ranma nor Akane is too happy about that. Jealousy and pride keep them apart, though after a while it becomes obvious that they love each other.

Ranma also has strong enemies in Tatewaki Kuno, Ryoga Hibiki and Mousse, they're all excellent martial artists and want to fight Ranma (usually, the subject of the fights are women...).