The three class combo statuses (Brittle, Staggered and Disoriented) each have an icon that is given whenever they are mentioned on the ability description pages. Like so (apologies for the colour contrast, but the game's UI is dark):
Whenever a combatant is suffering from one of these statuses, they have a three-dimensional version of the icon floating above them. For example, here's an opponent that is staggered:
The easiest way to take advantage of the class combo statuses is to configure your party members' tactics so that they respond to an enemy who has the relevant status with a relevant ability.