Re Arthur C Clarke,
He also wrote "The Fountains of Paradise" that deals with the construction of the elevator itself. First prerequisite is something like monofilament/bucky balls carbon, as any steel will collapse under its weight, second is a jolly big mass to anchor it in orbit- asteroid ideal.
To build it you start at the asteroid and work down, in fact you just extrude it out of the factory in the asteroid, anchor it to the top of a small mountain on the Earth to get you ouyt of the worst of thre weather. Once it's built the energy cost to get to orbit is something along the lines of $1 per kg, but if you are bringing products from orbit down, it can be effectively free.