Interesting question. I would say a few different things-
1. Dream Interpretation (this is my favorite of course). Our dreams reflect who we are-- even the parts of us that we try not to acknowledge. Our dreams allow us to take a glimpse into who we truly are.
2. Journaling daily and reflecting on a period of time. We often gain insight into ourselves when the emotional reaction to a situation has subsided and we are able to look at our written expression of that moment. Often times we are surprised about how we felt in the past.
3. Get feedback from others. Although not 100% accurate, getting feedback from a few different perspectives can help you see aspects of yourself you cannot see for yourself. If you keep getting similar feedback that you disagree with- this may be something to really think about. Are you being honest with yourself?
4. In general, a lot of people will tell you to "take inventory" of yourself. There are actually a lot of books and articles on the subject- perhaps because it is part of 12 step recovery. Taking inventory is a way you understand what you are actually doing. Typically articles will ask you questions that, if you answer as honestly as possible, will help you analyze yourself and understand where you need to make changes.
I hope that was helpful! Feel free to check out my hubs. I love new readers and am eager to get more comments, questions and feedback.