How Does the General Public Conceptualize the Global Climate System?

The answer is conceptualize.

Here's why:

The sentence asks about the way the general public thinks about or understands the global climate system. This requires a verb that describes a mental process.

Conception (noun): A conception is an idea or a belief. It's the result of thinking, not the act of thinking itself.* Conceptualize (verb): This verb means 'to form a concept or idea of something.' It's the mental action of understanding and forming a mental picture.

Therefore, the correct sentence is: 'How does the general public conceptualize the global climate system?'