The United States was structured to be a system of checks and balances, meaning each branch of government "checks" the other. For example, when Congress passes legislation, the president may sign it into law or veto it and send it back to the Capitol. The legislation must also pass the constitutional review of the Supreme Court. While the President of the United States is often believed to be the most powerful person in the country or even the world, this is not necessarily true. It's worth noting that the president does have numerous unencumbered powers. For example, they can pardon people convicted of federal crimes and issue executive orders that do not require Congressional approval. However, there are several ways in which presidents have tried to increase the power of their office.
First, the political landscape of the legislature can make or break an administration. For example, a Democratic president might not get as much as they'd like to done with a Republican-dominated House and Senate. Public opinion, then, is a pretty big factor in how effective a president could be, so many presidents don't stop campaigning once they're in the White House. Theodore Roosevelt was famous for his persistent campaigning for favorable public opinion. Presidents may support candidates for the House or Senate that would support their ideas or appoint cabinet members or Supreme Court justices who would further their agenda.
Presidents have also employed executive orders to expand their powers. For example, George W. Bush asserted that the idea of the "unitary executive" protected the president's orders from congressional or judicial oversight. Many presidents have held a similar idea, resisting the limitations Congress or the Supreme Court may try to levy upon their orders. Executive orders may at first seem to be presidential overreach, but many have been effective throughout history. For example, Abraham Lincoln used an executive order to enact the Emancipation Proclamation.