How can a star create a black hole

The strength of gravity is not just proportional to mass, but inversely to the square of the distance. A star collapses, that is they key. Fusion ceases to occur (which is the driving force behind its expansion and its relatively low density). Once fusion stops, it collapses under its own weight. The mass draws nearer and nearer the center, density increases. Density increases, volume decreases, and so distance decreases. Distance decreases, gravity increases, the mass becomes more dense yet.

The infinities are based on our limited knowledge of what happens inside the event horizon of a black hole. Once all the mass is squeezed and crushed by gravity small enough that the escape velocity on the surface exceeds the speed of light, there is nothing that we know of which can prevent further collapse. Hypothetically, then, all the mass will be continue to collapse to a single point, a singularity with zero volume and infinite density. But as I indicated, there are probably other factors that will come into play at some point before that. Because of the extremes involved, general relativity applies as well as quantum mechanics in that event, but mathematically they also do not agree with one another. Something is wrong with our understanding of them, therefore.

Basically most of the star's mass is compressed to such a tiny radius that its gravitational acceleration increases enormously. Looking at the equation for gravitational acceleratrion --
A = G * M ÷ R²
'G' is the gravitational constant
'M' is mass
'R' is radius