The seperation of powers is achieved in the new constitution in the United States by establishing a three branch system. This means that the federal government has three distinct parts including a legislative, judicial, and executive branch. Each of these branches performs different duties and has the power to check the other branches.
For example, the legislative branch (aka Congress) has the ability to make federal laws. However, the executive branch (president) and judicial branch (Supreme Court) can check the power of Congress. The executive branch can veto a bill while the Supreme Court can rule any laws that violate the constitution as illegal.