4 modest recommendations to share with those who embark on the blessed path of Sri Ramana Maharshi's Self Inquiry [1]:

(1)
Do it softly, effortlessly, let the I-thought reveal itself, don't push, no effort, peacefully. Effort happens to only do the opposite: it obscures the "I feeling" from your observation with mental noise.

(2)
The "I-thought" is just a name trying to depict this feeling of I that has always accompanied you. It can also be called I-feeling, I-sense. Use whatever label you feel at ease with. It's simply an intimate feeling of I. As you have the mental image representing someone else when you are thinking of him/her, referencing him/her, or being with him/her, you have the same type of mental image within your mind that represents yourself. At the beginning, you might wonder "what the hell do they talk about?" but when you spot it for the first time, and you will, I promise you, wow, you will immediately recognize it as something that has always and constantly been with you intimately in your stream of consciousness, always, hidden there at the bottom of everything. It has presence, it has energy, it has a footmark, it has a "smell", once you spot it consciously, you will find it very easy to track it again, you passed the hard stage of self inquiry.

(3)
At some point, when the "I-thought" is clearly perceived as an object apart of you, the one who senses it, ask yourself softly, calmly, silently: who is the "I" who watches this "I-thought" object? Do not try to analyze or rationally answer the question, just follow the pointer in the feeling that is instantly invoked by the question to feel the new "subject", the new "I" who perceives the previous "I" as an object. Do not hurry to make this move, you will feel when it is time to make the shift. Do it with time over and over again but please, do it softly...

(4)
Each time you observe an "I thought" you break your identification with this "I", you disconnect from this "I" as being part of you. This is the magic of observing (as you cannot observe yourself - if you observe something than it is not you...). Therefore, doing over and over the process in (3) you peal from yourself, from stage to stage, more "I" shadows, from gross "I"s to more subtle "I"s. At some point, after doing the back shifts to the observing "I" over and over as explained in (3), you will find yourself spontaneously abiding in some tranquil center, a reduced observing subject, a minimized "I" in which you could cease observing and just be, just abide in the subject, in the "I Am", not caring or being annoyed by any mental object including any "I thoughts". As a matter of fact, you will notice at this point that no "I thought", no feeling of "I" as an object is presently sensed. You have reached the point of abiding in the self. Just be there. Do not force it or try to articulate how to make it permanent. Just be there. After some time, the mind will take over again, this is natural, do not be frustrated. Return to the practice of (3) over and over. And again, do it softly with no stress or expectations. With practice, you will find it much easier to abide in this state of "I Am" and for longer periods, sometimes directly without even passing through the back shifts of "I"s as described in (3).

Remember: no effort, no expectations, no hurry...