If you are 15-16 and you have a reason to move out and a place to stay how would you go about doing so

Depends on your location.

Until you are 18, you are the responsibility of your parents. You cannot enter into contracts or move out on your own.

Some areas have laws allowing minors to apply for emancipation (ANY question on law needs to include your general locale as laws vary by area.) Generally it is very difficult to get a court to approve emancipation.

If you have a problem at home, then you may want to talk with family services about getting out.

What is the reason to move out ?