I have a friend who is renting a house in Tennessee, but there is no lease. The renter wants them to move out because they have someone who wants to buy the house. How long does my friend have before they are forced to leave?

Give them 30 days written notice served.. not handed to them.

No written ease means its legally a month to month lease.

The process doesn't change if there is no lease. They would be considered periodic tenants and subject to treatment as such. In TN that means 30 days prior to the rental date. So if rent is due on the first, they need to be given written notice 30 days prior to 1/1 as the earliest they have to be out.

http://landlordtenant.uslegal.com/lease/tennessee-termination-of-lease-for-month-to-month-tenancy-law/

If they do not leave by then, then the landlord would need to go to court for an eviction order.