Civics class was almost a half century ago. However, I thought I was taught that only Congress could make laws. How and why does the President have the authority to make law via Executive Orders? What are the limits of this authority?
Technically speaking, executive orders are not laws. While they might have the force of law, they are meant to clarify how officers and agencies of the executive branch manage the running of the federal government.
An executive order cannot make a law out of thin air. The Supreme Court in 1952 with Youngstown Sheet & Tube Co. v. Sawyer took this opinion after Executive Order 10340 by Harry Truman was challenged. Instead, the Supreme Court said that an executive order should clarify or expand upon existing legislation. So much so that since then, each executive order that has been issued by a president has come along with an explanation of what existing legislation they are acting under.
Nonetheless, executive orders are still criticized because they can be abused by the president, because even the caveat set out by the Supreme Court can be extremely open to interpretation.