Black holes are not really "holes," but are rather best described as a gravitational anomaly. The theoretical black hole is a point in space which is so massive that the object has literally collapsed in on itself. In terms of actual size, a black hole is very small; however, its mass is often that of a very large Blue Giant star, which has collapsed on itself, unable to support its own weight anymore. There are several theoretical ways a black hole can be formed; for now, let's discuss the most accepted and most commonly known: the collapse of a large star.
Our own star, The Sun, will not turn into a black hole when it dies. It will go through the same basic phases as the stars that do give birth to black holes, but its mass will not be nearly large enough, and its collapse will ultimately result only in a dwarfed, dying star. A Giant Blue star, however, does have the mass to go through the necessary phases to create our black hole. As a star ages, it fuses its compound elements together with the extreme pressure and heat built up inside of it. However, the star itself only has so much fuel, and when it runs out, it begins to contract, with no fuel to keep it burning and expanding.
Once the star contracts to a point, though, the pressure required to fuse the next heaviest element is acquired, and the star begins to use this as fuel, expanding once more due to the newly found intense heat within its core. This happens numerous times, until the star eventually reaches an element that it can no longer fuse. When this happens, the star will soon collapse on itself in a catastrophic event: a Super Nova. This event is so magnificent that it can be seen from neighboring galaxies and will bombard nearby solar systems with intense radiation and heat.
Should the star have been massive enough, a black hole will be left behind. However, if the star did not have enough mass, then a Neutron Star will have been born: a star that is, as its name suggests, comprised entirely of neutrons that are packed as close as they physically can be. This star is super-massive, but physically small when compared to its former state of being. Since gravitational pull is dictated by an objects mass, and not its size, the small, but incredibly dense, star continues to pull debris, dust, and gas towards itself with its strong gravitational field.
There comes a point, however, when this Neutron Star can no longer support its own weight. It becomes so dense and its weight is so great that it collapses on itself a final time, yielding the black hole. The black hole's mass is the same as (or greater than, as it continues to pull objects towards it with its awesome gravitational field) the neutron star it was born from, and so objects continue to orbit it and drift around it. The Event Horizon, the point from which even light cannot escape its pull, grows in size every time mass is added to it. However, the black hole's physical size cannot be measured, but is estimated to maintain the size of a pin head, or smaller.
Theoretically, any point which creates the same amount of gravitational pull can also produce a black hole. At the center of our galaxy is a massive star cluster that is said to have a black hole in the middle of it. Even though there were no known super novae in the past of our galaxy, this black hole exists. It is thought that the black hole exists because of the gravity of the entire star cluster reacting in the middle of the cluster, creating enough gravitational distress to produce a black hole.
Likewise, some scientists theorize that with enough energy, one can also create a black hole. While still in debate, the idea of "micro black holes" has been floating around for some time, along with the theory that, when colliding certain particles at insane velocities with enormous amounts of energy, a laboratory may be able to temporarily produce micro black holes. This has not been tested as of this date, however, and exists, as with the rest of the world of black holes, in theory.