I've had plenty of experience teaching and obviously lessons are different for different people but they will go a little something like this:

Introduction: I'll introduce myself and ask a few questions on swimming ability, experience. The more info I can get, the more I can help.

Assessment: From here on I'll be constantly assessing you without you even realising, but to start off I'll assess what you've told me. If it's a child that's taking lessons I'll assess them on the things they need to do to pass the stage.

Work: Then it's on to the actual teaching. I'll teach whatever I think needs attention or work on anything specific you want me to. If your a beginner, water safety and confidence is key. I'll adjust anything that's causing problems, with a big focus on balence, body position and breathing (under water).

After each lesson, I'll ask for a little feedback.