Spirituality comes when it comes. Jung thought that it happens during the second part of one's life, after one has learned how to deal with the external world and begins to look deeper into oneself.
I was always philosophical but not necessarily spiritual. My journey began, ironically, when I began reading about modern physics, Rhodes' Making of the Atomic Bomb
, and Hawking's A Brief History
. There was no goal to become spiritual, but slowly I was brought into a more complex world as my awareness of all that surrounded me began to grow. I began to notice things and have experiences (e.g. synchronicity, dreams, Taijiquan), that began to make me think much more about everything I use to take for granted: e.g. where did inherited characteristics really come from? How does a four year old play Mozart with no lessons?
A lot of awareness came from my health practices, and my study of how the body naturally keeps itself health. So slowly, I became less physical and more spiritual in my view of the universe and it came from many directions, sort of coalescing in a new way of looking at things so that everything work together and was very symmetrical - sports, health, perspective on life, hobbies, etc. The puzzle all fit together.
I think for most people it comes naturally at its own time and own pace, and everyone seems to be different.