Normal Force

"Normal" here means perpendicular, not ordinary. The force points straight out of the surface, which is why it tilts with a ramp instead of always pointing up.

It has no formula of its own. The AP Physics 1 equation sheet prints nothing for $F_N$. You get it from Newton's laws, by writing the perpendicular direction and solving. On flat ground with nothing else pushing vertically, that gives $F_N = mg$, and on an incline it gives $F_N = mg\cos\theta$, which is smaller. Neither is a rule to memorise; both are results of the same one-line balance.

It is not the weight. They are equal only in the special case where nothing else acts perpendicular to the surface and the acceleration in that direction is zero. Press down on a book and the normal force rises above $mg$; ride an accelerating elevator and it changes without your weight changing at all. A scale reads the normal force it exerts on you, not your weight, which is the whole reason you feel lighter as a lift starts down.

It is a contact force, so it disappears the instant contact does, and it can only push. A surface never pulls an object back toward it.

The procedure for every case, flat, ramp and elevator, is in how to find normal force, and weight vs normal force works the distinction directly.