When inserting the data if you want to set time portion to midnight, you can use TRUNC. For example, to add current date at midnight:
INSERT INTO TableName (DateColumnName) VALUES (TRUNC(SYSDATE));
As Prerak also pointed out you can handle the time portion also when selecting the data. For example:
SELECT TRUNC(DateColumnName)
FROM TableName
WHERE TRUNC(DateColumnName) < SYSDATE