This book heavily informs my views on RPG psionics.
It tells the story of Matthew Keller, a human miner/colonist, on a planet ruled, in perpetuity, by the descendants of the ship's crew that brought the colonists to that planet.
The story's protagonist is the stereotypical 40 year-old virgin. While not an unattractive man, the ladies always end up losing interest in him. The reason? Unbeknownst to him, he has a psionic power that allows him to become (effectively) invisible to others. His power is a little more complicated than that, but this should give you a general idea of his psionic power.
The novel tells the story of how, through the use of his psionic power, he is able to infiltrate the headquarters of the planet's rulers, and overturn the oppressive order imposed on the colonists.
My preference on the operation of psionics in a RPG setting mirrors the idea of an everyman (or woman) who has some vague idea that they are "different". That difference is the possession of latent psionic powers.
In an earlier post on psionics, one of my readers made the following remark:
"Follow me here... In a fantasy setting, I could conceive of a non intelligent, unwise, uncharismatic player or npc possessing wild and dangerous psionic ability (like a child or some hermit or crazy hillbilly). I always thought some of the most fun, interesting, and terrifying, aspects of psionic power was the unpredictability it may have in the hands of a person who doesn't really know how to handle it (think firestarter, carrie). I don't think psionics should be seen so much as an art form to be learnt (like wizardry), as an organic occurrence that a character has or not. Whether they can learn to control, direct, or fully make use of it is another question that may be determined by the balance of their intelligence, wisdom, etc."
I agree about the wild, dangerous psionic ability, although I would tie the class to an attribute, in this case, Charisma. In A Gift From Earth, Matthew Keller has a psionic talent, of which he is largely unaware, and has difficulty controlling. Through the course of the novel, the Protagonist discovers and perfects the use of this psionic talent, and discovers further applications of that talent (ie. additional psionic talents).
The Psionicist class in my 0e supplement would start as their own class, basically an everyman (woman), and would incorporate the idea of a latent psionic talent. I call this the Psionicist's "Wild Talent", and would be the psionic ability that the Psionicist starts with, at first level.