How does a Venus Flytrap know when a fly is on it?

It doesn't have to. It just begins the slow process of digestion, and at some point the insect prey will expire (unless it escapes).

Most predators, animals as well as plants, do not wait until their prey is "dead" to begin consuming it. In the case of larger animals, they are usually deceased, but not always. Sharks and snakes swallow some prey whole, and in rare cases the prey (such as recently eaten fish) have been found still alive inside.