How is the separation of powers and system of checks and balances laid out in the Constitution functioning in practice?
The Founding Fathers were very explicit in the debates about and drafting of the United States Constitution that they did not wish a preponderance of power to reside in any one branch of government. That is why the Constitution stipulates which branch is responsible for which functions. Clearly, the president, as Chief Executive and commander-in-chief of the Armed Services, would be the most powerful individual, but the Constitution's drafters fully intended that the other two branches of government, Legislative and Judicial, be equal in power to the Executive branch.
In practice today, there is a constant tug-of-war between the Executive and Legislative Branches for influence over U.S. foreign and domestic policies. Whereas the president presides over a vast system of departments and agencies employing tens of thousands of civil servants, to say nothing of the hundreds of thousands more serving in the uniformed military, the Constitution stipulates that it is the Legislative Branch that has authority over the federal budget, taxation, the power to declare war, and control over interstate commerce -- all tremendous responsibilities.
The Judicial Branch -- the federal courts -- holds tremendous responsibility for adjudicating constitutional disputes, but it tends to be more independent from the other two branches of government, as was intended to ensure its independence and integrity. On a day-to-day basis, discussions of the separation of powers and checks and balances involve the other two branches.
In practice, while Congress holds considerable power over the federal budget and can block presidential nominations for important government positions, some would argue that the Executive Branch has become dominant. While Congress passes legislation it intends to become law, the balance of power inside the two Houses of Congress almost always precludes it from being able to override an anticipated presidential veto, thereby limiting its influence.
The president, in contrast, can essentially make his own laws through what are called Executive Orders and Findings. By issuing, without the consent and sometimes even the knowledge of Congress, Executive Orders, the president can and does direct government agencies to perform certain tasks that might otherwise be opposed by the majorities in Congress. Executive Orders may prohibit U.S. citizens from doing certain things, and may involve the covert or secretive use of the military or intelligence community. Most importantly, Executive Orders carry the force of law. Violating the terms of these documents can lead to prosecution and prison time.
In sum, then, the system of separation of powers, with its checks and balances, has not worked as well as the Founding Fathers would have likely hoped.