As you use your psychic abilities, you will gain experience for them and will be able to upgrade them through meditating (accessed by pressing at the landing zone).
Simply complete and upgrade the four Paths of Enlightenment:
Path of Body – Body snatch a lot of people.
Path of Mind – Cortex scan a lot of people.
Path of Space – PK a lot of people, cars, boxes, etc. (just PK-throw a lot of objects)
Path of Time – Not available til you have the Temporal Fist ability. Once you have that, use Temporal Fist on a lot of people.