The holy book may be one, but it has not mentioned how to pray, at least not in any significant detail. We are told to pray "…as He has taught you that which you did not know", and the manner in which He has taught us was through the example of the prophet.
The same can be said of many Islamic practices; the Qur'an gives us general commandments, but one needs to look to the prophet for the finer details of implementation.
At the time of the prophet, this was a trivial concern; people knew the prophet personally and could emulate his actions, or ask him directly when they were unsure. For the first generation of Islam, the teachings were spread by these people who learned directly from the prophet. We no longer have that privilege.
The different madhahib came into being because there were differences in opinion on how best to reconstruct the prophet's example from the scattered, misheard and (in some cases) outright falsified evidences that were proliferating among the Muslim ummah in the later generations. All the schools have the same goal, to learn and apply the prophet's true teachings, but short of new Revelation they are still only human endeavours and susceptible to error.