If your school doesn’t have its own exchange programme, the best way to make your dream come true is to turn to one of the many exchange organisations. They often have many years of experience and can guide you through every step of your trip. Do some internet research and compare the different offers. You can request or download catalogues from most organisations to get a good overall impression.
A language test, a preparation seminar, help with organising all the important travel and insurance documents before you leave, the flights (maybe with Lufthansa if possible?), the selection of a suitable host family and school, support in the host country and provision of participations certificates – these services are normally all included in the packages.
Normally you would stay with a host family during your exchange. You share their day-to-day life and experience lots of great things with them. There is no such thing as a typical host family, because like anywhere there are considerable differences between families. Everything is possible, from a single household to a large family with dogs, cats, goats and horses.
Over time you will bond more and more, and by the end of your stay you might have even developed a lifelong friendship.