In short, you need to award a soldier 1 medal of each kind, before attempting to test for Psi-Abilities. Once accomplished, proceed with the testing, equip the Psi Armor and designate the soldier as the Volunteer.
There are 5 types of medals, each type available in small numbers, which you in turn need to reward a soldier one of each kind.
The medals are:
Urban Combat Badge (4)
Defender's Medal (3)
International Service Cross (2)
Council Medal of Honor (2)
Star of Terra (1)
Once a medal is awarded the action cannot be undone, thus the absolutely safest way is to save 1 medal of each type until you have tested 1 of your soldiers positive for Psi-Abilities.
Take note that medals can be made available once more, however that includes having the soldier in question killed as well as fulfilling the specific prerequisite; the Star of Terra being the sole exception. Also, any soldier with a high enough Will, about 80+, is practically guaranteed to have Psi-Abilities. The Iron Will option purchasable from the Officer Training School also help tremendously to boost the Will when a soldier is promoted.