How do scientists know that black holes exist

Well today at school we watched a video about the universe. One of the things it talked about was black holes, and it explained how when a star dies out all of its gravitational pull comes inward, trapping everything including light. Since it traps the light, it said we can't see black holes but scientists have enough proof to say that black holes exist. That really puzzled me because it moved on to another subject after that. If scientists say black holes exist, what proof do they have?

There are a number of things.

1. Simply the absence of light
2. Gravitational effects on light that is coming to us from an object whose line of sight to us is near to the black hole (the light has to pass close by to get to us) this is called "gravitational lensing"
3. Material that is on its way into the black hole spins around it (like water down a plug hole) we CAN detect that material.

It's pure logic.

The greater the mass, the greater the gravity, and therefore ergo we figured out that if enough matter came together in a certain amount, the gravity pull would become strong enough to pull things into it at the speed of light (and eventually even greater than the speed of light, which is weird, because nothing can go faster than light) so that no light would escape, and the phenomena would have certain characteristics surrounding it that, although enshrouds the black hole from prying eyes, provides evidence of it's existence, for nothing else could possibly cause the phenomena that surrounds black holes except black holes, and we've found evidence of such surrounding phenomena in the universe.

It's a no-brainer of logical inductive and deductive reasoning.

The first indication was when they discovered a dark region in space where objects that were objects were orbiting it, calculating it's size and mass from the orbits of those objects they realised it's gravity was so strong it's escape velocity would exceed the speed of light.