Yu-Gi-Oh! GX Duel Academy puts you in the role of a new recruit at the Duel Academy. You start your adventure, like most noobs, in the Red Slyther dorm. It is here you will meet many of the Reds from the series (like Jaden). In the lowest level dorm, you will get to challenge a few people to duels in an attempt to earn duel points (which are used to buy cards) and train for your exams.
Basically, the overall story of the game has you going to different locations on the academy island. You will visit the volcano, ocean, dorms and the Academy itself, facing each opponent. Every few days, you will find yourself in an exam where you will have to pass three tests in order to up your rank.
These tests fall under Written Exams, Timed Duels and Practical Exams. Written Exams test your technical knowledge of Duel Monsters. Here you will be quizzed on everything from fusion combinations to your knowledge of monster effects. The Timed Duels test your ability to work under a deadline. Can you get your opponent's life points to 0 by the time the clock reaches zero? These typically come off as a puzzle test. From what I could tell, there is always a solution; it's just a matter of using the right cards in the right manner.
The Practical Exams pit you against one of the teachers. Here you will not only have to face tougher-than-average opponents but typically there is also some other condition involved. For instance, your opponent may not be trying to knock out all your points, but instead have a deck that focuses on building up their own defenses. If you do well enough in your exams, then you up your rank.
Increasing your rank is good because you will move from the Red dorm to Yellow Ra and eventually Blue Obelisk. With each increase in rank you achieve, you will be able to face more opponents in more locations. This increase in duels ups your duel points and your skill. Ultimately, your goal is to earn the rank of King of Games.
When in a duel, the board and layout all look like any "Yu-Gi-Oh!" gamer would expect. Like I said before, this game doesn't introduce any unusual gimmicks; it is by-the-book "Yu-Gi-Oh!" CCG.