: I got to thinking that, scientifically speaking, how would one work? How
: people are transported from one end to another, and how the space end
: would align perfectly in respect to the ground.

Wikipedia is always a good start.

Rather than the weight of the structure being supported from below like a regular building (compression), the weight is supported by a counterweight well outside geostationary orbit (tension).

There would be vehicles that would pull themselves up this structure to get into space. Which in the long run would be much cheaper per Kg of payload than current methods. You can only go one way at a time, so you have to build multiple ones for simultaneous up/down or divide time into special up or down periods.

: Science fiction? Or can it realistically be done with the right things?

It's science fiction. There are several unsolved problems. The biggest one being money :P