When certain characters "class up" at the end of the battle screen, this indicates you can learn new skill or magic. Go to the menu, select the character that "classed up" and select "Skill". The magic/skill menu will appear, displaying both the learned magic/skill and skill/magics that have not been learned. Choose the one you want to learn and pay the "SP cost" to get it.

Note: You get SP by attacking and , killing enemies.