I'm no expert, but I'm quite interested and where's what I've gleaned:
We know that gravity increases with mass and we know the equations that govern this.
We also know how much force protons and electrons can stand up against before they get crushed together into neutrons (when a massive star goes supernova the core pressure exceedes this and a neutron-only star is left behind.)
Well, neutrons can only take so much pressure before they are crushed together. I believe this is called "neutron degeneracy."
If you take the gravity that is present by nature of the amount of mass of super-massive stars and run the numbers, it exceede's the force that neutrons can hold themselves up against and they crush down into a single point.
Despite being crushed together into a single point, the mass and hence amount of gravity of all of that mass remains the same. But now it's in such a compressed space that it's escape velocity is faster than the speed of light. Hence it theoretically looks like a black hold in space (no light is coming out of this crush of matter.)
The sphere where the pull of gravity is so strong that light can't escape if what I remember reading is correct is on the order of the size of a small star up to the size of Earth's orbit around the sun depending on how much mass is in the black hole. So on cosmic scales they aren't that big themselves.
Einstein theorized that gravity was a bending of space and that was later proven when a star was observed in a different location in the sky during an eclipse. Our Sun's gravity had bent the stars light (the effect can be somewhat inaccurately compared to seeing distortions in images as heat rises off of the street during a hot summer day.)
Black hole's gravity is so intense that just beyind the sphere where light can escape, is probably an area where the stars look all distorted and smeared around (by an effect called gravitational lensing.)
Other than their mass and rate at which they are spinning black holes have no other defining characteristics - size aside they are all similar because they have not characteristcs other than their mass (which directly affects their size and pull) and their spin. I think Steven Hawking was the one who coined the phrase "black holes have no hair" meaning they are all alike.
When matter gets pulled into a black hole, it is pulled with such intensity that as the particles slame into each other they become super heated. As a result black holes are surrounded by spheres or disks of super-heated matter which puts off a lot of radiation. That is a telltale sign of a black hole (at least one that is near other matter.) As it sucks more mass in, it grows by that very amount.
Most galaxies are thought to be anchored by a central black hole.
One theory says that black holes evaporate over rediculous amounts of time. In the quantum world photon and anti-photon pairs can spontaneously pop into existence out of the blue. As long as it's for an unimaginably small time scale the universe can violate the law of conservation of energy and mass this way. These photon - anti-photon pairs immidately annihilate each other and vanish. It was theorized by Steven Hawking that as this happens around the perimiter of a black hole (the event horizon) that one of the photon - anti-photon pair can get sucked into the black hole and the other pops free off into space. If this happens the black hole is decreased by the amount of energy in the escaped photon. Over rediculous amounts of time the black hole can shrink down as it's energy is slowly carried away by escaped partner photons.
That's the stuff I find interesting off the top of my head. I also tried to mention some things that are different from the facts that you find mindlessly repeated all of the time.