I've been studying, practicing, learning, and teaching Matsubayashi-Ryu karate-do since 1972, first on-base at Patrick AFB, FL and then in a small strip mall off A1A in Satellite Beach under Palmer Shihan. I've taken breaks, sometimes long breaks, but I always keep coming back.
From day one I have been told karate has a core of spiritual development, not religious development but spiritual development. While this doesn't exclude religious development it is not a focus.
In spite of this, in dojo after dojo, I have found very little emphasis on true spiritual development. This is most frequently due to the Sensei's above me also not having been trained in spiritual development.
When we go back to the source, Osensei Nagamine, we see he did not separate spiritual development from physical development. Osensei said "Ken zen ichi nyo" roughly translated means "Zen and the fist are one". His karate practice paralleled his spiritual development via Zen Buddhism and Zazen meditation.
Why spiritual development?
Excellent question and one which lends itself to an answer via metaphor.
Existence is like the ocean. We are all a part of the ocean of existence but occasionally we begin to develop into a wave. It is insanity for a wave to think it is somehow different, better, superior to the ocean it is a part of. Many times the wave can lose itself and believe it is more - it is not; we are not.
Even as a wave we are still part of the ocean and, eventually, every wave returns to the ocean, returns to the source we never actually left.
Every karate practitioner starts as a drop of water in the ocean, we grow, excell, become a wave and in that moment run the risk of losing ourselves in the insanity of the "superiority of the wave".
Eventuality even the greatest karate practitioner slows down, time & age draws us back into the ocean like it does everyone.
If we avoid the insanity that enticed us when we were the wave, we return to the ocean like going home. If we succumbed to the illusion presented by "wavehood", we return to the ocean fighting tooth and nail.
Fight or not, we all return. The difference is how we return, how we embrace our existence, our life, our death.
This is the spiritual lesson "hidden" in karate; do we visualize reality as a threatening enemy to be fought against or do we embrace the ocean of reality as the bed of existence we all come from and return to without every actually having left it?
So how do you incorporate spiritual development into karate training?
It's not easy because we, as Westerners, do not want to "waste" dojo training time on spiritual development.
We have to present spiritual development as an integral part of karate training. To that end, why no start with what we already do?
We do formal sitting at the start of every class; an ideal time to start.
A Warning; If you are not trained in Zen do NOT try to teach Buddhist meditation. To do so would present a tremendous danger to your students. As a psychologist I will tell you it is very easy to find yourself in an abreaction which will NOT end well.
However you can start with basic Mindfulness Based Stress Reduction (MBSR) exercises. Don't reinvent the wheel, you can download free self-help audio recordings of the exercises from the UCLA Mindful Awareness Research Center http://marc.ucla.edu/body.cfm?id=22 . If you like it; get certified as an instructor.
A note of caution: Screen your students. Any student under a physician's care for hypertension, heart disease, lung disease or any other chronic physiological or psychological ailment(s) should be cleared by a physician before starting the training.
Its a start. If it works for you, then find meditation instructors in the area who can help your dojo. A good source are your local Buddhist centers and/or Yoga centers - do your research.
Return to the source! (TFYQA!)