In Apocalypse, Psy training take a long time. To raise it in combat, you must succeed in doing whatever you try. There is one kind of unit who is particularly good at Psy attack, the half human half Alien race you must have good relation with before you can recruit any of them. They really suck in physical combat tough, so what I usually do is give them the best armor I have but give them the Marsec flying red torso. They should not go too fast at first, but when they fly their speed is regulated so they won't get so tired so fast. I always give them my best one hand pistol (usually Marsec plasma pistol at first) and they fly around doing pot shot Psy attacks and using their gun when needed (usually specially on Brainsuckers. If you're not high enough they can jump you, but otherwise they're out of reach and will still always try to get you.
Only the half Alien race have psy skills high enough to be able to field immidiatly for Psy attacks. The best shot is, of course, when you take control of another Alien. What I usually do is remove the shield, throw it away on the ground in my direction and make it fire on his friends.
