How do you go about evicting a tenant without a written lease in the state of Georgia when he has broken all of the verbal agreements?

Georgia Eviction Laws - Associated Content - associatedcontent.com

It lookz liks you have to give them 7 days written eviction notice. Then you go to court if they still won't leave.

Georgia Evictions

Whether the lease is verbal or written, doesn't matter. You need to follow the process for your area.

A lot depends here on whether the tenant is up to date on the rent or not. If he is in arrears, then 5 days after rent was due you can give them a 5 day notice to vacate. If they don't vacate within the 5 days, you have to file for an eviction order in court. A summons is issued which the tenant has 7 days to answer. If they don't then an eviction order is issued.

If they aren't in arrears then they will be considered a tenant at will:

44-7-6.
Where no time is specified for the termination of a tenancy, the law construes it to be a tenancy at will.

In that case, you may be required to give 60 days notice:

44-7-7.
Sixty days´ notice from the landlord or 30 days´ notice from the tenant is necessary to terminate a tenancy at will.