Well, there is no fixed start date of World War II only fixed dates of the smaller wars inside the total conflict. It's true that France and the UK declared war on Germany when they invaded Poland but by the media of the time it was referred to as a ghost war or a phony war(the french called it a joke of a war). Ofcourse that all changed when Germany initiated "Fall Gelb" and attacked the Benelux in order to properly invade France.
The war activity went full force from that moment on. When the US bombed pearl harbour you could say that the glocal fighting activity had reached its peak. Most of WWII was over when Germany declared an (forced) unconditional surrender. The conflict then was between Japan and the US, the UK(India and other colonies), the Netherlands(Indonesia) and later on Russia(which made a deal to attack Japan 3 months after the surrender of Germany). War ended 3 days after the invasion by Russia I believe when Japan surrendered after the atomic bomb on Nagasaki.