Farcaster technology was given to humanity by the TechnoCore and no human has ever been capable of truly understanding the mechanism behind the technology.
Farcaster portals are operated through phased singularity globes in orbit. The core AI's had revealed that farcaster singularity spheres are capable of bending the space-time continuum, connecting distant places together. Smaller farcasters also exist, including door-sized portals capable of being installed in buildings; some wealthy estates consist of rooms located on multiple planets and connected to each other via private farcaster.
Later all the singularity globes were destroyed at the command of Gladstone, so that the Technocore wasn't able to prey on the minds of the humans which where stepping through it anymore. This event is known as The Fall and destroyed the Web and the Hegemony. After this event none of the farcasters worked anymore, but after Aenea's escape from Hyperion she is able to go through the farcasters of the River Tethys, because they are being activated by an unknown entity, probably Lions, Tigers and Bears.
SPOILER ALERT! The section(s) below are MAJOR SPOILERS.
Aenea's Teachings revealed that contrary to the explanation given by the Core AI's, the Farcaster system was not actually made up of many connected farcaster portals, but rather, a single entry door to Planck Space, manipulated across space/time to provide the illusion of many doors. Furthermore, while to humans a trip through the farcaster medium was instantaneous, due to the timeless topography of Planck space the subjective dwell time there could be as long as the core wanted, enabling the Core to utilise the minds of human travellers during their transit in a huge core-created neural network for the computing purposes of the core. 
As revealed by Aenea, it is possible for an individual to farcast between locations unassisted by any technology, provided that the individual in question is attuned to The Void Which Binds. The only known way to acquire this ability is to become "infected" by the nanotech virus carried within Aenea's body. It is stated by Aenea that Jesus of Nazareth, the central figure of the Christian religion, had also attained the ability to freecast to some degree.
- ↑ The Rise of Endymion, 1997. Chapter 17