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The anime version of One Punch Man is really accurate on regard to the manga so nothing has been revealed in the manga that hasn't in the anime.

As you mentionned, in the manga, Saitama followed what he would call a hard training every day :

  • 100 push-ups
  • 100 sit-ups
  • 100 squats
  • 10 kilometers every day
  • no air-conditioner

Saitama training

As a result, Saitama loses his hair, and becomes incredibly powerful.

This training is the source of his power. Keep in mind that One Punch Man is intended as a shonen parody as it is making a parody of its codes.

In a lot of shonens, training is a main part of the manga.

As an example, in Dragon Ball, the sayans spend years in the Hyperbolic Time Chamber in order to become stronger.

By making the training of Saitama so simple (compared to the heroes capacities), One Punch Man is making fun of this Shonen code. Therefore we may not expect any more explanation on what Saitama did in order to become stronger.