A common mistake will be to conduct internal enqury "who am i?" as a purely mental exercise. Instead, find a sense of self in the chest ( Sri Ramana recommends practicing on the right side of the chest, from the zone where third rib connects with the chest bone. The sense of self on the right sort of "collects" itself in this area). This sense, known in old scriptures as Mahat, the great principle, is like a direct line to Brahman, unified pure consciousness. Some teacher recommend just to sit in this sense, solid like a rock, till by it's own power it will absorb you in itself and resolve into Samadhi
However, you may speed up the process. From the zone of the sense of self in the chest near the right side of the chest-bone, follow the sense of self inward, into the inner space, towards the center in the core of the chest known as Spiritual Heart. Here, the idea of self is purified from all the coverings, from all associated thoughts or images, from all memories or affects. A sense of intimacy, and stillness devoid of thoughts awaits the practitioner there. Attention sort of drops backwards and slightly down, into the core of the self, where only the meaning-"I am"-ness persists, with no distinct thinking about the self. One experiences the selfhood purified of all aspects except for it's core essence, "am"-ness of the self.
As this gradual reduction of the self-sense towards the core of the self takes place, continue absorption with one-pointed intention, to see, feel, experience where from this "am"-ness is rising from.. When attention becomes established at the very origin of attention itself, and at the very origin of thought, pause and examine what remains of the self. Experience may remain devoid of the sense of God (or anything ultimate) until the practitioner gives internal greetings, either by God's name, or simply by saying “Om”, the sacred syllable. In Vedanta, there is even a term for this phenomenon, jeda (inert) samadhi, i.e. experience of undifferentiated consciousness which is devoid of God. One doesn't find this detail in Sri Ramana's writings, only in the oral tradition of Advaita Vedanta . Do not be concerned by who is the one greeting, and whom do you great; just the act of it turns the experience of pure subjectivity into alive Oneness.
Different lineages of Vedanta complement each other in terms of recommendations for the practice. The following instruction for stablization in the Self comes from Sri Ranjit Maharaj. Maharaj did not describe it, but rather, demonstrated how to do it, so the description below is mine and created off his demonstration:
After you found the Self (alive Onenness), practice simply sitting in yourself, like a rock. Through this practice, self-awareness will mature.
May all the beings be blissful!
Namaskar