The prophet said "Pray as you have seen me praying and when it is the time for the prayer one of you should pronounce the Adhan and the oldest of you should lead the prayer." (bukhari no. 604)

So the way we pray is an imitation of the way the prophet used to. The words and actions of the prophet complement the quran in that they provide further explanations and rulings, so for example, prayer is made obligatory in the quran, and the timings of them are mentioned, but the actual way of prayer is shown only by the prophets actions.