Good question! There are many ways to deal with the business side of teaching, which you probably found out in your research. You may have to try a few different ways and see what works best for you. Here are a few things that I do:
Payment: I have students pay by the month. I used to have them pay for each lesson as they come (which eliminates the problem of cancellation, make-up lessons and sickness) but then you have the problem of people just not showing up. I know teachers who use a tuition plan for the school semester; however, most of my students would not be able to afford to pay in a lump sum.
Cancellation: I always try to be flexible with students if they occasionally need to reschedule a lesson, but they must call 24 hours in advance. Otherwise, they will pay for the lesson anyway, unless of emergencies or car trouble.
Make up Lessons: If I need to reschedule a student due to an unavoidable commitment, I try to make up their lesson as close as possible to their scheduled lesson. If that becomes impossible, I have a few days at the end of the month I schedule make-up times.
The point of having policies is to help communication regarding appropriate ways of dealing with problems, and making known the way you want to deal with issues. You need not be heavy-handed about it, but be firm about enforcing what you decide to do. It must be fair for each student and it helps them know what to expect. Once you have stated the “ground rules”, it is easier to be consistent. I strongly recommend you print your policies and hand them out to each student. That way everyone has the same information, and you don’t forget to mention something important to a new student.