L.F.
You decide what you want per hour or per session. I would do it by the hour. Make sure you write it all in the email so that they are completely clear on what you are charging, how to be paid etc. Here is an example:
Dear ______family,
Thank you for choosing me to be your daughter's tutor. I am available on ____days and from ______time to ___________time. My fee for tutoring is paid in cash at the time of service and _____dollars per hour/session etc. I have a 24 hour cancellation fee. If you book an appt and can not make it, I need at least 24 hours notice or you will be charged the full session fee of _______dollars. Thank you for understanding. If you have any questions, please call me at _________. Thank you and I look forward to seeing you soon.
Do not do a trial session for free to see how she likes etc. That is a recipe for disaster and she may take advantage. Have EVERYTHING in writing and have YOU sign and date it and have HER sign and date it. It needs to be a contract.
FYI- I said cash, but you could to check after the first visit if you feel comfortable. Otherwise, I would stick with cash only.
Take care,
M