Placed in service date: the date when the property is ready for rent. It is usually the date you put the property out for advertisement.
Depreciation basis is the acquisition cost of the structure (not land) by the date of placed in service date. Usuallly it is a percentage of your purchase price of the property, plus all money spend for improvement before placed in service date.
The depreciation starts on the placed-in-service date. Google partial year depreciation for method of calculation for the first year.
