What does it mean to "think"?

What do you mean by think?
There are actively two components at the root level of what people mean when they say "think". The first is the active verb, to think. The definition of this "think" usually boils down to: the development of a particular set of ideas or beliefs. The second is the scientific definition, or the set of chemical reactions that fire synapses and neurons. While it is impossible in function to divorce the two, in practicality the first one is the one that most people reference when they reference "thinking" a certain way.

"Thinking" in the first context is the process we actively engage with. Why someone has a specific belief, why they like certain things, how they live their day to day life, and how they see the world are in large part due to this "think". The second usage of "think" is involuntary. To ask a person why they thought in the scientific fashion is the same as asking why they poop or breath.

How does someone think?
There is usually some base to the way in which a person "thinks". For some people, it is worldview. Their outlook, goals, and morality all fit into this one framework. For others, it is a personal philosophy that takes on the totality of their lives. Do not harm, do unto others, and live in the moment are a few common ones. For the rest it is an objective goal that makes up the totality of their reality.  Subsistence, a better/specific job, or just being a better person can be the goal of these individuals. This is not to say that their lives involve less "thinking", it is just to say that their thoughts are focused in reaching that specific goal.

How does one think "X"? 
"X" can be anything from thinking better, to differently, to more complexly. The philosophical schools of epistemology, logic, reason, and rationality all have to do with the ways in which people think. In education you have theory in relation to personal philosophy, praxis, and pedagogy. The only wrong answer to "X" is correctly. While there are innumerable thoughts that can be wrong, there is usually something correct in the process that creates those thoughts. By adjusting, and not discarding thought processes, a person can become a more complete "thinker".