Sometimes intuitive information comes in the form of a sudden insight, but the way I practice it's more often a process of carefully attending to sensations, images and sounds and letting them form into something meaningful.
Honing your intuition is a lot like learning a language. The building blocks of the language are the raw sensations and perceptions that enter your consciousness. The amazing thing is that you don’t need to study what these sensations mean. You can actually learn to decipher them by simply noticing them and letting meaning form. It’s quite natural, but getting out of the way and learning to really allow the meaning to form, rather than trying to interpret it can be a challenge. I find it helpful to think of intuition as a language that teaches itself. By noticing what you feel and how our feelings correspond with the other world, you can begin to understand you feelings as a personal internal language.
When I teach "intuitive practice" I am really teaching people how to discover their own intuitive languages and processes. These are already in you and they want to communicate with your conscious mind. You just need the patience and openness to let them teach you.