How did the writers of the u. s. constitution put into practice the idea of separation of powers? a system of checks and balances?

The writers of the US Constitution put into practice the idea of separation of powers by establishing three branches of government: the executive (responsible for the enforcement of laws), the legislative (responsible for the passage of laws), and the judicial (responsible for the deliberation of laws). These separate powers then became imbued with the system of checks and balances where no single branch can act completely independently from the other. Take, for example, the appointment of Supreme Court judges. 

Appointing a Supreme Court judge is a responsibility of the President, the head of the executive branch. The president will pick a judge thereby influencing the judicial branch. However, the choice must first be ratified by the legislative branch, thereby giving them a deal of power in deciding who is going to become a Supreme Court judge. So there you can see that all branches have a role in this process, none of which can occur without the other branch having an impact.