You want to select the properties that are not leased. Those are the ones
that have no record where today is between the Arrive and Depart dates.

SELECT Properties.*
FROM Properties
WHERE NOT EXISTS
 (SELECT Leases.LeaseID
 FROM Leases
 WHERE (Leases.PropertyID = Properties.PropertiesID)
   AND (Date() >= Leases.Arrive)
   AND (Date() < Leases.Depart));

If subqueries are new, see:
   How to Create and Use Subqueries
at:
   http://support.microsoft.com/?id=209066

An alternative approach would be to:
1. Create a query based on the Leases table.
2. Drag PropertyID into the grid.

3. In a fresh column of the Field row, enter:
       Date()

4. In the Criteria row beneath this:
   Between [Arrive] And ([Depart] - 1)

5. Save the query.

6. Use the Unmatched query wizard (first dialog when you create a new query)
to make a query selecting the properties from the Properties table that are
not in that query.