Furusato Nozei is a donation that people offer to the local or prefectural government of their choice and in response, many municipalities repay the donors’ generosity by sending them "thank you gifts". In most cases, the gifts are local specialties.
Foreign residents of Japan who work and pay taxes here are just as entitled to participate as the Japanese.
Many youth exchange programs bring foreign teenagers to Japan, and the country also has a number of very active university exchange programs.
You can contact your local Japanese embassy or home university's exchange program department for information on how to proceed. Before contacting the authorities, read this short article and see which scholarship is within your reach.