If you've learned a spell/ability, you then have to 'Equip' it in the abilities menu. This basically assigns it as an option for your ability quickslot toggling ('up d-pad'). Once you have the desired spell/ability on the quickslot, hold R2/Right Trigger. It takes some time to cast certain ones such as healing.
Most magic is used in this way, though others take an effect automatically once equipped.
Hope that helps :)