How do black holes form?
There are three types of black hole and each is formed in a different way.
First of all we have never directly observed a black hole. Black holes are predicted by the Schwarzschild solution to Einstein's General Theory of Relativity. Observations of energy emissions and the orbits of some stars can only be explained by the presence of a small dense object which can only be a black hole.
It is thought that some black holes were formed in the extreme temperatures and pressures soon after the big bang. These primordial black holes are a candidate for dark matter.
Stellar black holes are formed when a star over 10 time the mass of the Sun reaches the end of its life. When the stellar core is predominantly iron fusion reactions can no longer take place as creating elements heavier than iron by fusion requires and input of energy rather than releasing energy.
When fusion stops the core collapses under gravity. The collapse overcomes the electron degeneracy pressure and atoms can no longer exist. Protons get converted into neutrons, positrons and electron neutrinos. The neutrinos cause the outer layers of the star to explode as a supernova. The core becomes a neutron star.
If the core is massive enough it overcomes the neutron degeneracy pressure and collapses into a black hole.
The thirds type of black hole is the supermassive black hole. These are in the order of millions of solar masses. It is thought that most large galaxies, including our Milky Way Galaxy, have a supermassive black hole at their centres. Supermassive black holes are probably formed by the merging of other types of black hole.