Any voice lesson should first and foremost emphasize your vocal health. Many popular techniques damage the vocal cords and oftentimes the damage is permanent. Sometimes even surgery will not reverse the damage.
To sing well requires a good understanding of human anatomy and physics as each relates to the production of sound. To sing really well also requires an understanding of music theory. Singing professionally adds the requirements of being able to sight-sing, learn music quickly, master expression, and understand performance behavior. These skills take many months or years to master, and thousands of hours of study. It’s unrealistic to think that talent alone will suffice; singers need skill mastery and many untalented but highly-skilled singers have rewarding careers.
Your lessons will begin with posture and breathing. These are skills that must be mastered before proceeding, because all the other skills depend on these being correct all the time. Once you are ready for the next step, you will learn the interaction and understanding of the dozens of muscles that influence the sound of the voice. This skill requires a very high degree of physical awareness of your musculature and many singers drop out at this point because they find the awareness emotionally uncomfortable.
Only when physical mastery is complete will your lessons include music. At this point you will study sight-singing, music theory as it relates to singing, and practice techniques. You will learn songs that are not intended for public performance as many singers slip back into bad habits when they begin singing, and those bad habits must be replaced with new ones. When you are comfortable with reading music and have shown that you can apply your new techniques, you will begin to learn songs that you may want to perform in public; however, there are still more skills to be learned before you can expect good results singing in front of other people.
Your lessons are completely private and will never be recorded or shown to anyone without your explicit written permission. The only time I would ever discuss your lesson is to talk with a doctor or other health professional after you have signed a HIPAA consent form, and that is to discuss only the physical aspects of your singing.