To add just a little, the star has to be pretty massive (classed a supergiant), or several hundred thousand times the size of our solar system's sun to be able to collapse into such a point singularity. Even then it may simply form a "neutron star", which is a very small (it would fit on a teaspoon), but very very dense (in the order of 10000 times the mass of the earth).
I haven't read up on black holes in a long time, but I'll give a simple (Newtonian) description of what I remember: the force of gravity is actually dependent on mass and distance. In effect, the larger two masses are, and the closer they are to one another, the more the gravitational attraction there is between them.
So when a supergiant star burns out, it will explode in a supernova and all the mass will collapse upon itself. The denser this mass is, the more likely it will form a black hole. You can thus think of a black hole as something that was just so dense that pretty much everything is attracted to it.
This way you don't have to think of it like a giant space-hoover :P
