About 2500 years ago a prince in India name Siddhartha set out on a quest to free the world from suffering. He left his palace in the dead of night accompanied by an attendant and his horse. Toward morning he shaved his head and said farewell to his attendant and horse and embarked on a six year study with two of the greatest spiritual teachers of the time. At the end of this period, and following intense ascetic practice, he came to the realization that asceticism would not lead him to liberation. He had practiced this intense asceticism with five companions who regarded him as their teacher. After Siddhartha turned away from asceticism he was abandoned by his companions. Siddhartha drank milk from a girl living nearby, sat down under a tree, and entered meditation, vowing not to arise until he had cut the roots of suffering. During this meditation he became enlightened. After two weeks, at the urging of several gods, he began teaching spiritual truth for the next 45 years.
At this point the sequence of events changes according to some interpretation. Initially Siddhartha, now known as the Buddha, the Awakened One, taught individual liberation from suffering as most of his disciples were ripe for that path. His five former companions all became liberated as Arhats in his first formal sermon at Deer Park, where he taught the Four Noble Truths. Later thousands of other people (and perhaps many, many thousands) attained Arhatship as well. This was the First Turning of the Wheel. The Theravadin teachings come primarily from these teachings.
Some years later Buddha taught the Second and Third Turnings of the Wheel, mostly on Vulture Peak. These teachings involved the true nature of all phenomena and the seed of Buddhahood that all sentient beings have. General Mahayana come from these two major teachings. Zen Buddhist is said to specifically come from a specific teaching during which Buddha wordlessly passed the Zen teaching on to Kashyapa (there was more than one Kashyapa in Buddha's entourage).
The Buddha is also said to have transmitted some Vajrayana practices at this time as well to a small handful of people esp. King Indrabodhi and a king (I think) from the earthly pure land of Shambhalla.
Following Buddha's physical death, there were three Buddhist councils, one immediately after his parinirvanna, one 100 years later and one about 100-150 years after that. Over time, differences emerged as different teachers emphasized different teachings (and thus practices) of the Buddha. However for several centuries people pursing the path of individual liberation resulting in Arhatship and people pursuing the Bodhisattva path (Mahayana) lived and practiced together at the same monasteries.
As direct disciples of the Buddha, and direct disciples of those direct disciples, and direct disciples of those direct disciples died, people began recording the teachings of the Buddha in writing rather than orally. Lineages began to diverge and have some disagreements on particular points ....