What do you bring to the table? This is typically an uncomfortable thing to think about or discuss, but at the end of the day you are always bringing something to the table, whether intentionally or not, and you should be aware of what you’re bringing. Be comprehensive in your answer to this question: include both the good and the bad. (One thing to watch out for is leeching: try to give more than you take when possible).
Who am I to others? This is one of the most important skills to have, and one of the most difficult skills to learn. This is important because you are rarely who you think you are to others–you might think you are being nice, but other people might think you’re mean due to differences in values, interpretation, perception, etc. One way to get an idea of who you are to others is to ask for honest [anonymous] feedback. Another way is to replay your interactions with others, and imagine what you would think if you saw yourself behaving and acting the way you did. (Explaining may sound like complaining, constructive criticism may sound like insults, etc.)
Responsibility. Always take responsibility for what you can. You are responsible for who you are, you are not responsible for how people react to who you are, but you should take their feedback into consideration. I used to think people didn’t like me because they were bad people, but when I become more self aware, I realized I was being a bad person without knowing I was. Turns out people had legitimate reasons not to like me. Don’t blame others, take responsibility. If people react unexpectedly to something you do, either you don’t understand that person well enough to predict how they will respond, or you are not presenting yourself in the way that you think you are.
Don’t Be Self-Centered. While you should take responsibility for yourself, don’t go too far: if someone acts differently towards you, don’t be so quick to immediately blame yourself. People have lives outside of their interactions with you, so avoid falling into self blame, guilt, etc. Instead, emphasize with them by trying to see things from their point of view–what might be going on to cause them to act differently. Maybe when they made a face when they saw you, they just ate something sour, rather than they really don’t like you. (Read Nature of Your Own Identity)