How were trade sanctions against Japan the reason for starting World War 2 against the US?

Though it wasn't the only reason, the trade embargo deeply affected Japan. Japan obtained the majority of its resources (especially fuel and oil) from other countries. By blocking trade to Japan, who was already recovering from sever economic recession, they economically drained Japan.

As early as 1938 the US began a series of economic and covert military (Flying Tigers) actions against Japan. The largest was the cancellation of the 1911 commercial treaty with Japan. The Roosvelt administration increased these under Secretary of War Stimson and Treasury Secretary Morgenthau began a series of economic actions that gradually put a stranglehold on the Japanese. Among these was the Export control act which blocked all exports from US private companies to Japan.

In July of 1941 the Roosvelt administration launched a double offensive, by stationing long range bombers and moving the Pacific fleet towards Japan in Pearl Harbor, Wake Island, and increasing the Philippine military presence, (actions similar to the Missiles in October the US would face from Russia/Cuba years later), Roosvelt convinced both the UK and Holland to cut off all oil supplies to Japan.

These actions forced what Stimpson wrote in his diary as the actions he hoped for to force the Japanese to take the first shot. The Japanese did take action on December 7th by attacking the US base at Pearl Harbor and against the Philippines.