Like other Skill EXP, you gain Psionic EXP by just using the Psionic skills in battle. (Though they have to actually connect at hit the enemy.)
It takes a while to level up, as it's designed to fit into a much larger game.
Oh, I see, sorry!
You can acquire Psionic skills by using the chair in the east wing of your Safe House. There are many other upgrades there as well, that you can acquire by exchanging EXP.
The southern purple section of the upgrade area pertains to Psionic abilities, so you can find several there. Hope this helps!