From the View My Hero page, clicking the View Skills/Spells button brings you to the skills & spells page. It displays the current skills & spells you have trained in the first box. If you click the heading below it for your class training, it will display the skills & spells available in-class to your character.
For those wishing to train outside of their usual class skills & spells, you may do so as well! However, it will cost you double the training points to learn the chosen skill or spell. This is to represent the additional training time required to training the new skill or spell that is not native to your class.
As demonstrated by the screenshots below, this character is a knight and has "kick", "double attack", and "smash" trained.
When he clicks on the "Your Class" section he sees he can train his various stances, as well as "blitz".
But the knight is interested in bandit attacks and clicks the bandit class and sees that he can train the "circle" skill.
Upon clicking the circle skill the knight is brought to the skill detail page and sadly reads that he cannot train the skill as it is untrainable for out-of-class characters.