Read more about Individualisation from the works of the Mother and Sri Aurobindo.
Self Observation Summary
What is Self-Observation?
Man must know himself and discover and utilise all his potentialities: but to know himself and the world completely he must go behind his own and its exterior, he must dive deep below his own mental surface and the physical surface of Nature. 
As one goes beyond the ordinary surface body consciousness, we discover an inner level of mental, vital, physical being along with a inner subtle - physical being. By identifying ourselves with our inner being, we are able to observe our thoughts and feelings and can trace the source and motives of our actions and operative energies that build up our surface personality. This helps us in improving our self-vision.  It is only through self-observation one gets an intuitive perception of the Nature forces - sattva, rajas, tamas. By Observing one’s dreams, one can come to understand them and their significance to our inner life. 
Why is Self-Observation Important ?
In our everyday life, we always look outwards into the appearance of things and get trapped into the surface ignorance and rarely turn inwards to seek self and discover and utilize our potentials. ...if each element which comes with its ignorance, its unconsciousness, its egoism, is put before the will to change and one remains awake, compares, observes, studies and slowly acts, that becomes infinitely interesting, one makes marvellous and quite unexpected discoveries. 
To work for your perfection, the first step is to become conscious of yourself, of the different parts of your being and their respective activities. You must learn to distinguish these different parts one from another, so that you may become clearly aware of the origin of the movements that occur in you, the many impulses, reactions and conflicting wills that drive you to action. 
How to Observe Oneself?
By projecting oneself on a screen and then observe and see all that is moving there and how it moves and what happens.
Not fear, but vigilance. If you remain vigilant, then with the increase of the Force upholding you, a power of self-control will come, a power to see and reject the wrong turn or the wrong reaction when it comes. 
By Developing a Quiet Mind
If the whole mind remains quiet and detached observing the vital movement, but not giving its assent, then to reject it becomes more easy. This established quietude and detachment of the mind marks always a great step forward made in the sadhana. 
By Developing the Witness Attitude
In order to become conscious, one needs to develop within a part with a witness attitude that observes and is not carried away by thoughts and feelings. People with very developed introspective mind identifies with this part and it becomes easy for them to begin the process of self-observation.
The process of self-observation should be objective and one should look at oneself as a third person engaging in the surface level activities. One need not like or dislike the activity but sincerely observe the movements of nature.
By Education of the senses By the education of the senses the growth of one's general education is aided.In fact, they should be used for this, as instruments of observation, control and knowledge.  Consequently, all life is an education pursued more or less consciously, more or less willingly. In certain cases this education will encourage the movements that express the light, in others, on the contrary, those that express the shadow. 
Difficulties in Self-Observation
Be aware of the “escape attitude’’ as man always rushes into external action and looks for reasons to not have time to observe himself and turn inward.
There is “danger of ego” in observing the movements and attaching the sense of ‘I’’to the process of self-observing and not going behind the surface level I.
Surface -level observation It is evident that our state on the surface is indeed a state of knowledge, so far as it goes, but a limited knowledge enveloped and invaded by ignorance and, to a very large extent, by reason of its limitation, itself a kind of ignorance, at best a mixed knowledge-ignorance. 
Content curated by Aditi Kaul
Read more about Self Observation from the works of the Mother and Sri Aurobindo.