This is the must-have field type to show if a listing is avaible or not, and when it can be reserved. If you want to include the field with Date into Search, make sure you set to Yes the fields Show search range and Search support.
Calendar popup will let you select the date in Add new property section.
Do not miss out to add the new field into Search widget:
If you did everything correct, you will see the new field in your Search widget in the frontend: