How can I tell if I need a fuel pump on my car or if I need a new battery

I was stopped at a red light and when I went to go when it turned green the car just quit. I could not get it started. It had to be pushed to a nearby parking lot and then towed home. The tow truck man said I need a battery. Some say it may be my fuel pump. It sounds like it wants to start but will not turn over.