Most of the foriegn students in Japan have had a Japanese host family during some part of their stay. As for those who receive Japanese geovernment scholarships, many of them are assigned a host family when they reach Japan. For others, they can find a host family through their universities, town offices or other volunteer organizations.
The host family provide temporary accomodation to the student if necessary, and help him/her with the formalities. Most of the families keep in touch even after the students are able to manage things by themselves. They care a lot; some of my friends receive too much care. :-p
As for me, I was introduced to my host family by the International Liaisons Office of my university. Mr. and Mrs. Iguchi (whom I refer to as Iguchi-san and Keiko-san in my posts) are professional photographers. Iguchi-san, now retired, was a director at Mitsui Corporation, Japan.
Iguchi-san and Keiko-san treat me like a son. In our first conversation, Iguchi-san told me
"If there are things you like to do, or places you like to go, please let us know!"
Spending time with a Japanese host family is one of the best ways to learn Japanese culture and Japanese language. For me, I have more benefits: being photographers, they help me to improve my photography; they take me or provide information to visit places and events that are not so well known (such the horse races in my previous post); above all, I have a family here, who care.