There are two main camps of conceptual photographers: those who strive for minimalistic effects, and those who relish in business in their images.
The more minimalistic conceptual photographs are composed so that the focus is entirely on a single subject, a single concept, narrowing the viewer in on a single thought. Think of those clean white backgrounds upon which objects are placed in thought-provoking manners: no distraction from the idea.
The opposite camp is a little more involved. These are the conceptual photographers who place dozens and dozens of objects into their photograph, often to the point where there is no clear single subject. Rather, every object, every symbol, is placed to play off of another, creating sweeping conceptual landscapes of ideas that are both extremely specific yet also describe a broad message. You don't see such photos quite as often, as they take considerably more work, but they're certainly out there.