I am assuming that you have made the decision to send your child to private school. We have several articles on Private School Review which explain the differences between private and public education. If you still need help making that decision, then read those first. Then circle back and pick up with this first challenge.
2. Convincing your high school aged child to go to private school
The secret here is to make her think this is her idea. It cannot be anything which you thought up. You can certainly support her decision once she has actually made that decision. If you ignore my advice, you will probably end up with a very miserable teenager. I know that you know what is best for your child. You can certainly get away with that kind of unilateral thinking and approach while she is very young. But I strongly counsel against employing that approach with a pre-teen or teenager. The idea of going away to private school has to be her idea. Start well ahead of time with general discussions about high school and where it can lead. Listen carefully to her needs, concerns and wants. You will come to a common ground after a while. It will be worth it because she will embrace the idea and make it hers.
4. Deciding whether to go to boarding school or day school
5. Getting in
Yes, I saved the best - or worst depending on your perspective - to the last. If you need financial aid, then file your PFS as soon as you can. Financial aid pools are always limited. Don't miss any deadlines if you need to be considered for financial aid. Work tuition payments and the sundries into your budget. Keep things current. This video introduces us to financial aid in private schools and how it works.
You have several options including free schools. If you have been posted overseas, most large international companies will include schooling for children of expatriate employees as part of your package. Also, several dozen private schools over free or greatly reduced tuition for families with incomes below certain thresholds. Always ask about financial aid if you feel you need help.