Aside from using pusher sticks or blocks to keep your fingers away from the blade, the other critical element of table saw safety is understanding kickback. In the wrong circumstances, the saw blade can suddenly grip the workpiece and launch it back at you; the sudden change in force often causes the user to push their hand into the blade. Fortunately, kickback is a predictable and avoidable phenomenon if you understand the physics involved.
https://www.youtube.com/watch?v=8f8VWwtaudU