The authority comes either expressly from legislation or impliedly from the powers inherent in the presidency. Obviously, if congress gives the president authority to make orders, that's where the particular authority comes from. As for implied powers, let's take an easy example, the president as commander-in-chief. Is there any question that a commander-in-chief inherently has authority to issue orders to those he commands?
The rest of your homework you'll have to do yourself!