At the conclusion of the Not-self Doctrine, the Buddha describes the freedom, the emancipation, that is achieved with Enlightenment: 

Therefore, surely, O monks, whatever consciousness, past, future, or present, internal, or external, coarse, or fine, low, or lofty, far, or near, all that consciousness must be regarded with proper wisdom, according to reality, thus: ‘This is not mine, this I am not, this is not myself.’ 

O monks, the well-instructed noble disciple, seeing thus, gets wearied of form, gets wearied of feeling, gets wearied of perception, gets wearied of mental formations, gets wearied of consciousness. Being weary he becomes passion-free. In his freedom from passion, he is emancipated. Being emancipated, there is the knowledge that he is emancipated. He knows: ‘birth is exhausted, lived is the holy life, what had to be done is done, there is nothing more of this becoming. (Anatta-lakkhana Sutta)

Here it is important to note that despite previously stating that “consciousness . . . is not myself,” the Buddha proclaims that after emancipation the noble disciple knows that “birth is exhausted, lived is the holy life . . . there is nothing more of this becoming,” meaning that he knows he is Enlightened. Now, what the noble disciple knows describes an intentional consciousness:  

The necessary and sufficient condition for a knowing consciousness to be knowledge of its object is that it should be conscious of itself as being this knowledge. (Being and Nothingness, p. 10)

Therefore, when the Buddha claims that consciousness is “not myself,” he is not proclaiming that there is no person, no being, nor that consciousness is an attribute, a quality, of some other being. Consciousness is being: “the consciousness of being is the being of consciousness.” (Being and Nothingness, p. 69)

What the Buddha is in fact stating is that consciousness of the past, future, present, etc., are “not mine, this I am not,” that is, as ideas of consciousness, as objects of consciousness.  

But then what is this “myself” that the Buddha is referring to?  

The fundamental problem is that the consciousness of being is not any-thing: It is Nothingness. As Sartre explains, human consciousness, or what he calls the For-itself, is always what it is not:  

The being of consciousness, as consciousness, is to exist at a distance from itself, as self-presence, and this zero distance that being bears within its being is Nothingness. (Being and Nothingness, p. 128) 

It is the human condition to always not being any thing, and as a result, we always desire to become, to exist as some thing. This something is the self that we create from the objects of our consciousness: our physical form, materiality, our perceptions, thoughts, and emotions.  

It is this created self that is the primordial source of human suffering as we are perpetually trying to become what it is inescapably out of our reach. This constant striving to become the self we can never be is what Sartre calls Bad Faith:  

Try as I might to carry out the tasks of a café waiter, I can be one only in a neutralized mode, in the way an actor is Hamlet . . . What I am trying to actualize is a being-in-itself of the café waiter. . .I am the waiter in the mode of being what I am not. (Being and Nothingness, p. 104) 

Human consciousness, the For-itself, becomes a nothingness to gain existential freedom, free will. But this not- being-anything, this freedom of conscious being, is also our intrinsic existential Anguish:  

What we should note here is that the freedom manifested through anguish is characterized by a constantly renewed obligation to remake the Me. (Being and Nothingness, p. 73)

This is what the Buddha realized with heroic effort. It is by letting go of our attachments, our desire, for the world (the material, the thoughts, feelings, and emotions), that we regain our inherent freedom:  

The well-instructed noble disciple, seeing thus, gets wearied of form, gets wearied of feeling, gets wearied of perception, gets wearied of mental formations, gets wearied of consciousness. Being weary he becomes passion-free. In his freedom from passion, he is emancipated. 

This pure awareness of existing which is not anything of the world, as a Nothingness, can only be realized through the method of Buddhism, the Eightfold Path, as any description of this true Self would be just another idea and would eclipse true realization.