What is known about the years of oral tradition of the Pali Canon? With the Buddha teaching for 45 years before he passed into parinibbana, what is known about the methods and practices used to keep his teachings alive until they were written down? Do we know how many people were involved in this effort? How was such an extensive collection of teachings categorized?
Traditionally the original source of the teachings is Ananda. Ananda was the Buddha's cousin and primary attendant during a lot of his life up to the Buddha's death. Being 
so close to the Buddha, he heard at first hand the Buddha's teaching and was able to commit them to memory. Shortly after the Buddha's death the First Council was convened and Ananda was prevailed upon to recite all the Buddha's teachings he could recall. Fortunately for us he could recall a lot.

This is why many of the Pali Canon sutras begin with 'Thus have I heard'. It is Ananda speaking and recalling the Buddha's teachings from his own experience.

Example from the Mangala Sutta


  Thus have I heard. On one occasion the Exalted One was dwelling at
  Anathapindika's monastery, in Jeta's Grove, near Savatthi. Now when
  the night was far spent, a certain deity whose surpassing splendor
  illuminated the entire Jeta Grove, came to the presence of the Exalted
  One and, drawing near, respectfully saluted him and stood at one side.