No, there are no clear rules.
There is no constitutional provision nor statute that explicitly permits executive orders. The term "executive power" Article II, Section 1, Clause 1 of the Constitution, refers to the title of President as the executive. He is instructed therein by the declaration "take Care that the Laws be faithfully executed" made in Article II, Section 3, Clause 5, else he faces impeachment. Most executive orders use these Constitutional reasonings as the authorization allowing for their issuance to be justified as part of the President's sworn duties,2] the intent being to help direct officers of the U.S. Executive carry out their delegated duties as well as the normal operations of the federal government: the consequence of failing to comply possibly being the removal from office.
An executive order of the President must find support in the Constitution, either in a clause granting the President specific power, or by a delegation of power by Congress to the President.
That page discusses how the practice has evolved, but basically it boils down to "The President claims that a law requires him to take action". Sometimes the laws are more explicit, sometimes they're a significant stretch, and sometimes they're stretched so far they're challenged in court. But there's no absolute law on the matter.