Classes in ICT are explicitly designed to carry a lot of weight. They have their own rules, with the idea being that you need to learn the core rules, but beyond that you only need familiarity with the rules relevant to your class or classes.
In this sense, it's a bit like 4e, but unlike 4e, the mechanics are fairly terse. Perhaps unsurprisingly, they are designed to fit on a single index card. But despite this, there's a lot of flux in this design space - there are some guidelines for creating characters, but (much like equipment) there's room for some really crazy open ended stuff.
Also, probably unsurprisingly, there's a lot of Final Fantasy Tactics (and a touch of 4e) to be found in these classes. We'll talk more about what that means once we have a few examples under our belt.
Characters start out with a class level of d6 in one of the starting classes. Exactly what the starting classes are is something of a setting decision, but for purposes of illustration, we'll say that they're Squire and Chemist. When the character acts, he gets to add his class die to the pool for any combat rolls. Out of combat, if the class is not relevant to the roll, the player rolls a d6 instead.
As the character gains experience, he may increase his level die from d6 all the way up to d12. In addition to increasing the size of their die for rolls, leveling up can open the door to access new classes. Basically, non-starting classes have requirements that usually revolve around levels in other classes. For example:
Thief - Requires Squire d8
Knight - Requires Squire d10
Black Mage - Requires Chemist d10
White Mage - Requires Chemist d10
Paladin - Requires Knight d10 and White Mage d8
We'll get into how exactly those improvements are made when we talk about experience and advancment, but for the moment, just be comfortable with the idea that your class die is going to get bigger and as it does, it may open up the ability to switch classes.
Next, we'll start drilling into class abilities.
1- For players who like a more descriptive take on these things, the "levels" of a class break down as follows:
(no Adjective) d8
So a Squire d10 might also be called an Experienced Squire d10.