You'll notice. A dead goldfish isn't breathing at all, and they tend to look really stiff and may lay in the water at an abnormal angle.

well you can be sure because they sorta have their mouth open like their in shock and they lie very still at the bottom. you can tell when their dieing because the swim very fast and bump themself onto the tank sides and start to sink or they will apper stuck to the tank side. one guppy i had died like that. if they want to live and are trying to a few words for a few hours will work wonders. when i first got my goldfish they looked like the were going to die, but i changed the water every day and fed them a healthy diet. now they even pop their heads out of the water for food and look like new!