How the black hole is made
Answers
Black Holes are made when very large stars die. When the star runs out of fuel for nuclear burning in the core it is no longer able to support itself from collapsing under its own weight. The star first collapses and then the outer layers rebound to form a supernovae explosion. What's left at the core is a Neutron Star or a Black Hole depending on the initial mass of the star. To form a Black Hole the mass left at the core after the explosion must be more than about 3 times the mass of the Sun. The star for most of its life probably needds to be between 50 to 100 times the mass of the Sun to eventually form a Black Hole.
It is impossible that a Black Hole will form within several light years of Earth as there are no stars large enough in the neighbourhood. Some of the brightest stars in the sky may eventually form Black Holes, although not for millions of years. These include Rigel and Betelgeuse, both in the Constellation Orion. No-one can really predict the fate of an individual star exactly though because it is very hard to weigh them!
October 2002 Update: Many thanks to a Curious reader from Russia who pointed out that this answer only applies to stellar mass black holes. As you can find out by reading our topic page on black holes, we also know that supermassive black holes with masses many millions of times the mass of the Sun are found at the centres of many galaxies. The question of their formation is very interesting, and could tell us a lot about galaxy formation. Their mass seems to be related to properties of the galaxy (specifically the velocity dispersion in the bulge) leading to questions over which formed first - the black hole or the galaxy.
At the other end of the scale there are microscopic black holes (a black hole with the mass of the Earth would be about the size of your finger nail, and we're talking smaller than that). There have been some speculations recently that we may be able to form these in particle accelerators soon (this depends on how gravity behaves on very small scales which we're not sure of yet) or that they may form when very high energy particles hit our atmosphere. You can read an article about this here. Don't worry though, the tiny size of the black holes we're talking about means that they evaporate into hard radiation in a fraction of a second, and there would be no possibility of them swallowing the Earth (as suggested by some of the more sensational media sources).