If you wish to explore your thoughts through writing, you’ll simply have to write your thoughts on the paper. Besides its role in communication, constant writing can be very helpful for one’s intelligence and self-awareness, while also fundamentally recording your thoughts. This is how writing can be described: the conversion of thought into a series of words and sentences, and this is why writing is a most valuable and needed action if you wish to record your thoughts not only to yourself, but to others long after your death.
I can tell personally that thanks to my writing, I got to know myself better, and thus I became more self-conscious, analytical and introspective. It even changed my life, perhaps to a point of a mental rebirth. Writing can do a lot for one’s inner self-development, and thus can be a great possibility of giving to yourself many insights and words of wisdom otherwise you may miss. Even after you’ll die, perhaps your writing pieces can store your identity and your memory even for hundreds of years, whether you’ll become known or remain anonymous.
For a start I suggest you to write the names of all the subjects, people, opinions, experiences and other things which you think about them constantly. After you wrote this list, choose one or more of the subjects, and elaborate on them from whatever aspects you wish to. You can write without judgments, since restricting your writing shall only serve as an obstacle between you and your own wild stream of thoughts. Don’t be afraid to write about something which is perverted, inappropriate, suicidal or unmoral. By recording your thoughts you need to be honest with yourself, regardless of external opinion. This is why I also recommend writing the darkest of thoughts on paper, instead on the computer. No one can hack into your papers. As you’ll practice more and more writing, it will eventually become a very fluent action where you can free your mind from negativity. When I write for extensive periods of time, I myself feel more cleansed, satisfied and even in love with this intellectually-worthy activity.
Remember that it may be not easy as you may think it will, not because of the effort but because of the high possibility to confront anything within you which you dislike or even hate. This is why such a quest requires an immunity of a certain degree. Even if you may burst out crying or being furious - it is okay, as the writing mission you wish to work on requires the minimal of limitation as possible, if not no limitations at all.
Since our honest of thoughts can be dangerous or disrespectful, if you want to share what you wrote in the exploration of your thoughts, think deeply before you share the writing pieces. Most of the time, I believe thoughts are meant to be kept hidden from the naked eye if they are abnormal or even radical.
This is a most exalted quest to do with your life, as I believe everyone should know themselves more than just their names, origin, occupation and such - but to know one’s mentality, along with one’s psychological and philosophical life. This can only do good if you believe you are strong enough to face with the self beyond the facial expressions and of other’s expectations out of you. You’ll have no idea how infinite you are until you’ll write on a constant basis.