When travelling overseas how can I arrange to stay in the home of local families.?

You can check with the University near by your place. Go speak to the study abroad office or international student council office to get a better idea on host families. Also, see if you can access the newspaper of country you are planning to travel to. It might have ads on cheap housing or something. Look into Youth Hostels as well...

Good luck!

If you are a university student, then choose an exchange program with a homestay option.

If you are not a university student then you either need to find a travel program that offers homestays OR visit travel websites and find someone who is willing to allow you to stay in their home.