Unless you really understand Psychological Type and the nuances of the various personality functions, it's a difficult task to suddenly start to use iNtuition in an Extraverted direction. It's difficult to even understand what that means, much less to incorporate that directive into your life. With that in mind, Here are some specific suggestions that may help you to begin exercising your Extraverted iNtuition more fully:
Take care to notice what people look like in different social situations. Look at their hair, their skin, their makeup (or lack thereof), their clothes, the condition of their clothes, their shoes, their facial expressions. Don't compare others to your own appearance, or pass judgment on their appearance, simply take in the information.
Think of a situation in your life in which you weren't sure how to behave. Now try to understand how one or two other people would see the situation. Don't compare their behavior to your own, i.e. "she would know better than me what to do", or "why is it so easy for her, but so hard for me". Rather, try to understand how they would see the situation. Would it be seen as a problem, or as an opportunity? Would it be taken seriously or lightly? Try to determine their point of view without passing judgment or comparing it to your own.
When having a conversation with a friend or relative, dedicate at least half of your time to talking about the other person. Concentrate on really understanding where that person is coming from with their concerns. Ask questions.
Think of the people who are closest to you. As you think of each person, tell yourself "this person has their own life going on, and they are more concerned with their own life than they are with mine." Remember that this doesn't mean that they don't care about you. It's the natural order of things. Try to visualize what that person is doing right now. What things are they encountering, what thoughts are they having? Don't pass judgment, or compare their situation to your own.
Try to identify the personality type of everyone that you come into contact with for any length of time.