When does an hourly employee qualify for overtime, after 40 hours within one week, after x numbers in one day, or a combination of both? We are a new hotel in Mississippi with about 20 employees.

In Mississippi, as in most other states, it is only required after 40 hours WORKED (you don't have to include paid time off, holiday pay, etc.) in a workweek. You must define the workweek as beginning on a day/time certain.