The jury is still out, but since most large galaxies show signs of harboring one or more central black holes, I'd say they develop at the galactic core very soon after galactic formation.
How? Theory: a very large star - 100 solar masses or more - develops at the hub and quickly runs out of fusion fuel. Maybe it has one or more companions. Anyway, said massive star explodes, creating a supernova. All the material from the star's outer layers is blown outward, along with the outer layers of any companion stars. At the same time, the core implodes due to the lack of radiation pressure. It's so massive in itself that it cannot stop collapsing. It shrinks past degenerate material, past neutronium. It winks out of known existence, leaving only a "singularity", a point of infinite gravity. This warps spacetime. How big the sphere of influence depends on its mass.
As the crowds of stars, dust and gas get too close to the black hole, they get whirled around the accretion disk then get sucked in like water going down a drain. Thus the black hole grows.
If the infalling material overloads the accretion disk, some of the x ray-hot plasma will be thrown out along the spin axis as a jet thousands of light-years long. See the 10-17-02 APOD or look up Seyfert galaxies and quasars.