Constitutions can help with this (particularly with creating the formal structure of the state) but they cannot actually create the reality of the system. For that, it is the attitudes and practices of the people that are more important.
Constitutions can do a great deal to establish the formal structure of government. The Constitution of the US did set up the system of a bicameral legislature with a strong president and a Supreme Court. Even there, though, the Constitution did not state whether the judicial branch could rule that laws passed by Congress were unconstitutional. That is a pretty basic thing and it was not addressed in the document but only established by pratice.
Constitutions can do little to determine the way a political system actually works. Many constitutions of authoritarian states (the USSR, for example) guarantee political rights to the people. But if the society does not care about or push for those rights, they exist only on paper. A familiar example of this would be the rights of black people, guaranteed by the Constitution (after the Civil War) and routinely ignored until at least the 1950s and '60s.
Constitutions can set up formal structures, but they cannot actually create a state and they particularly cannot constitute the reality of a political system.