One can learn himself to think more deeply and philosophically through the practice of Autodidacticism. The meaning of Auto-didacticism is self-education or self-learning, or in other words, to be a teacher of yourself.
I don’t really think there is a more reliable and personal-adjusting method of deepening one’s thought than simply being alone for a period in your daily life, and simply contemplating on questions which you see important and valuable to yourself.
One of the purposes of thinking is to obtain and to process knowledge. Generally there are two main types of knowledge: knowledge that comes from exposure (learning new concepts, gaining more acquainted with a certain subject) and knowledge is translated to wisdom. In order to think, one needs to expose himself to a certain source of information (the internet or the library, for example) and the second is to use that knowledge in the process of your thoughts. When you use the knowledge you have in your arsenal to create something new (a conclusion, an opinion, even a book), you produce wisdom, and wisdom is the higher level of thinking, in which one can claim to be deep-thinking.
In my opinion, everyone can produce wisdom/deep-thinking out of every possible piece of information. Therefore, Deep-thinking is always possible. It doesn’t necessarily infers that only people with high enough level of IQ can indulge in such beautiful and appropriate action, because even a not-so-highly intelligent person can create something new out of the knowledge he has. This, is because every person has some short of knowledge at his hands. All one needs to do is to be aware of that knowledge, and ask questions that relate to that knowledge, which may create further questions, which, in return may create another knowledge, which is the answer one has reached.
You can use my answer as a source for deep-thinking, and even seeing an ant colony on the earth can get someone to think deeply. Thinking deeply is to find or create the bigger picture or meaning which lies in every piece of information. One can argue that there are more ways, however contradicting a statement is by itself the ability to create something new from an already existing entity and its symbolism. Thereby, deep-thinking/wisdom is an equivalent to art: you have the colors, tools and patterns in the form of knowledge, and the art you produce from it, can be identified as a form of wisdom: you create something new from an already existing resource, just like I said earlier.
Another and final thing: deep-thinking is expressed through a series of multiple questions and answers. A simple or ordinary form of thinking can be described as few questions and answers - even a question and an answer (if at all), and that’s it. This is not deep thinking because producing wisdom requires progressive and complex indulgent on a certain subject. The element which drives one to seek wisdom is mystery, or in other words: the unknown. Hence the purpose of deep-thinking is gaining knowledge over something you don’t know about. On contrary to simple thinking, deep-thinking is done independently or in an intellectual discussion, or brainstorm, and takes more time and dedication.