Psionicists use the same experience table as Magic Users. So, in order to achieve 2nd Level, a Psionicist must obtain 2,500 experience points, and so on.
At each level, after first level, a Psionicist may aquire up to two additional levels of psionic talent mastery. In order to obtain each additional psionic talent, the Player rolls a d20, twice. If both rolls are less than the character's Charisma, the character obtains two new talents. If one roll is less than the character's Charisma, the character obtains one new talent. If neither roll is less than the character's Charisma, the character obtains another level in their wild talent.
Once you have determined how many new talents you have obtained, you a d10 and consult the talent table. 3rd Level Psionicists can roll on the first or second column. 5th Level Psionicists can roll on the first, second or third column, and 7th Level Psionicists can roll on any of the 4 columns. If you obtain a result, but you do not have a talent in an earlier column, you must take the earliest talent in that talent tree, that you do not yet possess.
For example, at 5th Level, the Player rolls on column 3, and gets a result of 3, "Mass Invisibility". Since her character does not have "limited invisibility" or "invisibility" she must take "limited invisibility" instead.