Be observant of the world around you. In the business of daily life, it's easy to focus only on your own thoughts and the events that directly affect you, but try to make an active effort to pay close attention to what happens around you. Listen to conversations, read newspapers and simply watch for different causes and effects in daily life and reflect over them. Consider keeping a diary with your thoughts about what you see. The practice of thinking over and contemplating the world around you will increase your ability to make connections between your existing knowledge and the problems you hope to have intuitive insight into in the future.
Interact with others around you, such as your relatives and coworkers. Because so many of life's problems involve human beings, increasing your social network and experience of other people will help you to better understand how they think and operate. As much as possible, reflect over what you experience in your social life. Have meaningful conversations with the people close to you and try to understand the way they think. This will improve your instincts about people.
Increase your expertise level. Read books and attempt to expand your knowledge base in the area in which you hope to have good intuition. To a large degree, intuition is a byproduct of knowledge and experience. Having in-depth knowledge means that you have a wider base of reference when you're presented with a challenge in need of a solution.
Practice applying your intuitive skills in daily life. An example of an exercise in intuition is to read mystery novels or even watch mystery movies and attempt to predict how they will end. Usually these stories provide clues that a person with good intuitive skills can piece together before the end.