I have been thinking about this too, trying to figure out if I know myself. A couple things I am working towards are:

1) mindfulness. By this I mean becoming more self aware of what's really going on in my head and what's driving it. What things am I thinking due to past events that cause me to react in that way for example? My mind is a busy place and it's easy to get caught up in the storm and not really be thinking with my frontal lobe so to speak. In addition to what I am thinking, I am trying to be more aware of what I am feeling. Even if it's an uncomfortable or confusing feeling that doesn't make sense with the situation, just recognizing it in order to accept it and where I really am in that moment. Through this I can be honest with who I "am" at the moment, but have to work hard not to judge it or feel shame about it.

2) Considering my values and what I want. Once I accept where I am and the reality, then I can think consciously about what matters to me and how I want to define my life. This can then guide me when things get confusing, and can be a constant when I feel unsure of "who I am". To some degree I guess we can choose what we want to be.

3) Being open to the fact that the "self" is a concept that can, and perhaps should, change. Once I know the reality of who I "am" at the moment, and what I value and like or dislike, I can stand by that while being open to change and accepting new information.

Another thing to note is that I think this concept of self can change depending on things like culture. I listened to a podcast by a Native American who was talking about how the "self" is not really such a concept in their culture in the same way it is in some cultures, and how who they are is defined more by their relationship with others and the land. I may not be summarizing that exactly correctly, it's been awhile since I listened to it, but that was the general idea I think. I kind of liked that way of viewing it in a sense. It makes it less about focusing on me and more what I am a part of.