It works off of a point system.
You gain psy points for each level of your level (1 at 1st, 3 at 2nd, 6 at 3rd, &c.). You also again a bonus for high attribute for each level, but this is usually a +1, rarely a +2 for an 18. SWN uses an OD&D-like attribute bonus scheme.
There are 5-6 lists of powers which you have to acquire sequentially, 5-6 powers per list. You usually can gain one power per level, on occasion you can get two depending on level up choices (I think). A 1st level power costs one point, 2nd level 3 pts, 3rd level 5, &c. You can permanently invest points to keep a power continuously active, although not all powers are applicable.
So by 9th level you will have mastered one discipline, have a smattering of abilities from other lists, and probably 1-2 that are "always on". If I remember correctly, you always have enough points to use one level's discipline once. So a 7th level psion can use a 1st, 2nd, 3rd, and 4th level ability once per day, if desired. But, you can spend your points as you wish.