Help me understand how stored fat is used by the body?

Ok so I’m trying to visualize my fat. I have a good amount of fat around my belly. If I don’t eat, how does my body reach into this storage? I’m assuming the same way it was put in… but how was it put in?! What is dropped off by my blood stream? Are there veins connected and what not? If so, why don’t more people die of these fat build ups?