This is quite tricky one.Though spending day is never a problem,spending night is.Some of my suggestions are:
1.Have somebody as your interpreter:It may not seem that important in cities with many people knowing English,but in villages,it is a must.I went with my friend who was Indian and I really think that you cannot survive there without interpreter as it is quite possible that nobody may understand you.
2.Homestay:To be honest,if they don't know you,they will not let you spend night in their home.You may get lucky but please also heed my next point.
3.Safety:A big concern would be safety.There may be people who take you with them to their village and then may rob you.So,don't fall in such traps as such incidents may happen.
Considering the previous three points,if you don't know anybody in India,your best bet is to talk to the tourist department for this.There may be such programs for tourists.Another option is to befriend your guide or driver(who is registered by tourist department) and ask him to show his village as they normally live in nearby villages.Even then,you should take precautionary measures like validating his identity and sending his identity information to your local contact or something while he notices you sending(truly it helps).
Now if you are lucky to find somebody,some suggestions:
1.If you go to any village which is not a tourist spot,be prepared for a lot of people coming to see you(honestly).
2.Respect the ladies/girls.It is the most important thing you should keep in mind.
3.Don't go inside their worship place without permission,and if you get permission,don't go inside wearing shoes.
4.Ask them to prepare local dishes,I got to taste some dishes only in villages.
Note:I've heard that crime rate is less in South India,so your guide/driver would probably be a safe bet.