According to page 14 of the Psi World rule book, “The decision to be psionic or normal is left totally up to the player.” Absent some necessity of a particular campaign, why would anyone choose not to be psionic in a game that focuses primarily on psionics? That's like going to a nice seafood restaurant and ordering a cheeseburger.
Psionic powers are divided into major disciplines and minor disciplines. The Hammer Shall Strike adventure/supplement introduces the concept of marginal talents, otherwise known as 'Spot-on-the-Wall' psi. The main rule book says:
The vast majority of NPC Psionics in most compaigns [sic] have extremely limited or marginal psionic abilities, such as causing water to boil (one cupful at a time) or creating a ball of colored light. Player characters are considered to be part of the upper 10% of the psionic community as far as powers are concerned.
Hammer supplies more details regarding marginal talents; providing more examples and actual rules. Page 6 of Hammer says, “Nearly ninety percent of the people technically classed as 'Psionic' are of the [Spot-on-the-Wall] type.” This is a slight but unimportant difference from the figure suggested in the rule book. Hammer further states that psionic individuals with marginal talents rarely use their abilities (or don't use them at all) due to their lack of usefulness. Essentially, they live their lives as 'Norms,' not subject to the governmental restrictions placed upon more capable Psis. Close associates may not even know such a person is psionic; however, the government knows and “their identity cards do carry the notation 'Class III Psionic'.” Presumably, 'Class I' refers to Psis with major disciplines and 'Class II' refers to Psis with minor disciplines.
Most powers require an expenditure of 'power points.' The amount of power points that a character starts with is equal to twice her PSI attribute score; this is really the only purpose of the PSI attribute (except for increasing the chance of gaining additional power points). So, a beginning psionic character can have as little as four or as many as forty power points; the average amount being twenty-two power points. Power points are recovered only via sleep. A full eight hours of sleep is required to regain 100% of a character's expended amount of power points. Lesser amounts of sleep provide fewer power points; for instance, “7 hours 45 minutes” of sleep grants only 75% recovery. Napping won't help; a character needs at least three hours of sleep to recover 25% of used power points.
Abuses of power are checked by the finite amount of power points any given character has at his disposal. As an example, 'personal teleport' costs 20 points per use; the average beginning Psi will be able to accomplish this once per day.
Characters are able to acquire additional power points. A character may attempt to gain more power points whenever she “has used 250 power points in game situations.” So, if the average beginning character has about twenty power points, an attempt to gain more power points can be made after approximately two 'game situation' weeks – assuming the character uses most of her power points daily and she consistently gets eight hours of sleep.
Attempting to increase power points works similarly to improving a skill. The PSI attribute score is added to 100 and the current amount of power points is subtracted. The result is the % chance of an increase. If successful, the character can gain as little as one point and as many as ten with five being the saddle point on the probability distribution.
Each major discipline represents a suite of abilities. For instance, some of the abilities included with 'telekinesis' are: Move Object, Levitate, Heat, Cold, and TK Light. A character with a major discipline has access to all the abilities in the discipline to the extent he can afford their cost in power point expenditure. The rules allow characters to develop new variations of abilities within their major discipline (and within the bounds of game balance). For instance, a character with telekinesis might want to develop a 'walk on water' ability. Experimenting and learning to control the ability requires 30+3d10 days of practice, minus the average of the character's PSI and INT attributes. Such practice precludes any adventuring on the character's part. After the requisite period of practice, the character has a % chance equal to the average of PSI and INT to 'master' the new ability and use it during play.