This poor soul qualifies as a Hopeless Character with four below average attributes and two average attributes, but such is life. The highest attribute is Dexterity, so I'll make him a thief named Shufflo. It's really a nickname because he shuffles everywhere, except when he's on a job then he is light on his feet. No one but a fellow member of his Thieves' Guild would ever suspect him of being a burglar.
Rolling All Dice, my results were d4: 1; d6: 2; d8: 3 d10: 1; d12: 12; d20: 8.
The d4: Psychic Fuel
With a roll of 1, Shufflo's Psychic Fuel is his Strength. Each time he uses his Psychic Power, his Strength is reduced by 1 point (as if it wasn't low enough already).
The d6: Psychic Focus
With a roll of 2, his Psychic Focus is Wisdom. Unfortunately, he has little of that at hand, so his roll when using his Psychic Power will carry his Wisdom penalty of -1.
The d8: Psychic Rejuvenation
With a roll of 3, Shufflo is a bit luckier. The method by which his Psychic Fuel (Strength) is restored is simple immersion in water, which restores 1d4 points. This happens each time he immerses himself completely in water. To qualify for the rejuvenation of Strength points, he must be completely dry between immersions. He'd better not be a hydrophobe.
The d10: Psychic Enhancer
With a roll of 1, his Psychic Enhancer is crystal. Shufflo's grandmother once gave him a small crystal, telling him to rub it when he was worried about something, and it would put his mind at ease. Coincidentally, Shufflo's Psychic Power becomes easier to control when he is in the presence of crystalline structures, so every time he rubs that crystal as he uses his power, he gets a +1 to his Psychic Power roll, which negates his Wisdom penalty.
The d12: Psychic Failure Consequence
With a roll of 12, the consequences of failure to control his power result in physical injury. That's 1d6 hit points of damage each time he fails his Psychic Power roll. If he were wise (which, obviously, he isn't), he would wait to experiment with his power until he were more experienced or had an edge. Just what is that power anyway?
The d20: Psychic Power
With a roll of 8, his Psychic Power is Etherealness, the ability to become noncorporeal in the physical world, and even to travel to the Ethereal Plane of Existence. In this regard the Fates have been kind indeed, for here is a thief with the power to walk through solid walls. It may come with a risk, but here is a means for a burglar with no special talent to do the impossible.
Shufflo the Thief, a nondescript nobody who survives by stealing, has a secret talent, a Psychic Power, that enables him to walk through walls, perhaps even to pass into a higher plane of existence. He is a phantom, but his power weakens him, and he is not a strong man. Luckily, a simple plunge into ordinary water miraculously revitalizes him. He is not especially wise, but the crystal his grandmother gave him seems to help him control the power, so he is never without it. The power comes with a great risk, however, for should his control of it falter, his body may suffer grievous wounds.
[Edit: I changed the term "Wild Talent" to "Psychic Power." 2015-05-13]