Here is a good read on spirituality without faith.
Spirituality without Faith
If you scroll down to the Characteristics of Spirituality, it states that spirituality has three main features; an emotional response, cognitive context, and practice.
The emotional responses are intrinsically rewarding feelings that are sought out in their own right. These emotional responses can enhance the celebration of life or help us cope with life's losses. According to Richard Dawkins, we have an "appetite for wonder," an appetite for evoking the positive emotional states that are linked to our deepest existential questions.
The cognitive context allows us to invoke the emotional responses. They are a set of beliefs about ourselves and the world around us. It allows us to give meaning to life and appreciate the wonder, beauty, and deeper significance of life.
The third feature is practice. Sometimes we need ceremonies to elicit these deep experiences. Ceremonies such as song, dance, meditation, rituals, or a walk in nature.
As one of my friends in recovery says, "Spirituality is practicality". Spirituality is acquired through practice and action rather than theory or speculation. It is actually living a healthy and rewarding life rather than just yearning and thinking about one.