I would say the first step in strengthening your intuition is having the recognition and desire to strengthen it. Self-awareness is a key part of growth, as Tarot teaches us, but is absolutely essential to grow and develop your intuition.
Understanding the concept of intuition, having enough self-confidence to embrace intuition, and recognizing that we ALL have a sense of intuition has always been a challenge for me. With Tarot, for example, it was very easy for me to memorize the meanings of the cards and use them to "tell the story." It was easy to learn to have a conversation about the cards during a reading. But it was much more difficult to listen to that quiet voice or inner feeling regarding something you need to be able to communicate, know, understand, or think about. As someone who is much more confident in the physical world than wading into the spiritual, trusting myself and my intuition is something that has taken some getting used to. Being a father has certainly helped in that department.