The science of Yoga is meant for self-discovery, through 8 limbs of Yoga like Yama, Niyama, Asana, Pranayama, Pratyahara, Dharna, Dhyan, and Samadhi. A person can not explore Yoga fully unless one starts from Yamas and reaches to Samadhi. Most of the people think that Asanas (Yoga poses) are Yoga but it is only one step, and that is the 3rd one in the eight limbs of Yoga.

Some of the teachers might be very flexible and expert in demonstrating asanas with excellent teaching skills still they are considered as an asana teacher until they experience the stillness of the mind as Patanjali says “Yoga Chitta Vritti Nirodha”

Maintaining spiritual and healthy relationship in a Yogic way is the responsibility of teacher and student. On the path of Yoga, Teacher and student should be more aware of their energies and feelings. While doing Asanas, pranayama, meditation or day to day activities awareness is an essential part of every physical and mental activity.

Few points can be helpful for teachers.
Do your Yoga practice regularly.
Grow your experiences. On the path of Yoga, everybody is a student. Even you can be a world famous Yoga teacher. Try to be a student once a year, participate in some retreats or learn more about meditations. Come out of the role of a teacher.
Be Present in the class. Be aware what you say, how you move, how you adjust students.
Treat every student equally.
Be more creative in the class.
Keep your heart open.
Listen to every student and speak from the heart.

A few points for students.
Remeber that Yoga is coming from teachers to students for thousands of years. In India, in Yoga tradition teacher is considered equal to God,
Gurur Brahma Gurur Vishnu
Gurur Devo Maheshwarah
Guru Saakshaata Parabrahma
Tasmai Shri Guruve Namah

Try to understand Yoga Philosophy and its tradition
Read Yogic, spiritual books to expand your knowledge about Yoga.
Be aware of your energies, thoughts, and feelings.

Hari Om Tatsat!