In Oracle, you can simply subtract two dates and get the difference in days. Also note that unlike SQL Server or MySQL, in Oracle you cannot perform a select statement without a from clause. One way around this is to use the builtin dummy table, dual:
SELECT TO_DATE('2000-01-02', 'YYYY-MM-DD') -
TO_DATE('2000-01-01', 'YYYY-MM-DD') AS DateDiff
FROM dual