To be a deep thinker you simply have to get in the habit of asking deep questions about everything around you. What is a deep question? Let's look at a couple examples.
Suppose someone lies to you, and you simply explain it by saying, "He's a jerk!" That may be true, but it is shallow thinking. Instead you might ask why he lied to you. A deeper question than that would be why people lie in general, or why it is wrong to lie. Related questions might include whether it is ever okay to lie, and if so, when.
To become a deep thinker then, you have to get in the habit of looking beyond the immediate questions raised. Fortunately it isn't a heavy philosophical exercise to determine which questions are "deeper" than others. You will usually recognize them when you see them. For example, which is a deeper perspective, pointing out all the excuses a person makes for his or her behavior, or asking and exploring why people feel the need to make excuses?
Here's a good rule to remember: The more profound questions are those which have wider application. For example, knowledge about a particular man's personality, though perhaps useful, is limited and shallow compared to knowing the principles of psychology that apply to all people. Questions about a particular business are not nearly as deep as those about the principles of success which could be applied to all businesses.
Another rule: If one question or idea is an example of another, the latter is the deeper one. Water freezes at 0 degrees and becomes steam at 100 degrees. This is an example of the more fundamental principle that substances have three forms (solid, liquid, gas) depending upon temperature.
You can always start with "Why?" Like a child, ask it again and again, and question each answer. "Why do we force people to pay taxes?" Because they wouldn't pay otherwise. "Why wouldn't they?" They consider other things more important. "What are taxes for?" To serve the public good. "Who defines the public good?" The voters, by way of their representatives. "If the public votes for evil things are they still a public good?"
If you can remember to ask such questions often enough throughout your day, and continue doing it for a few weeks, it will become a habit. Making these "probing" thought patterns habitual is how you become a deep thinker. Carry a note to remind yourself at first, or put reminders on your schedule.
Being A Deep Thinker - The Use Of Language
Question even the language which you and others use, instead of taking it for granted. For example, what does "national defense" really mean? Does it mean protecting the borders, the government, the flag, honor, the people, or the rights of the people in the nation? These are very different ideas, and perhaps not always compatible, yet we often take for granted that we all mean the same thing when we use the words, "national defense."
The metaphorical nature of language is essential to growing our range of expression. We refer to the "memory" of a computer, and by using this metaphor it becomes easier to understand and communicate. On the other hand, this use of metaphor can also limit our thinking. The sun "going down" is a small example. We know intellectually that it is the planet turning which causes this apparent effect, but our language creates the impression that the sun goes away each night.
Now, if we stop and really consider that the sun never sets, all sorts of new ideas come to mind. Solar panels in space would always be in the sun, and they could beam electricity down to us by way of microwave transmission. Someday, a "nightless farm" could fly around the Earth at a thousand miles-per-hour, growing vegetables in 24 hours-per-day sunlight. These ideas may not be new, but they only occurred after mentally questioning the idea that the sun goes down.
Finally, a deep thinker recognizes the representative nature of language in general. Words are only meant to point at things in reality. They are not things by themselves. While this may seem obvious, it is forgotten in common discourse. A man says that corporations are evil, for example, and another jumps to "prove" this idea wrong, rather than trying to see what the first man is pointing at with his words.
You may recall the ancient puzzle called "Zeno's Paradox," which "proved" that motion is impossible. Because of the perfect logic with which it was demonstrated, some chose to believe that what we see as motion is an illusion. Much later, philosophers, mathematicians and physicists found acceptable challenges to the paradox, but the real lesson here is that logic isn't infallible because language is imperfect, and if we are to more fully understand the world, we have to allow for that. A deep thinker, then, uses words as the valuable but limited tools they are, while trying not to let words use him.