PHP and MySQL: Order by most recent date and limit 10

use:

SELECT * FROM notes WHERE note_author_id='$u_id' ORDER BY date_time DESC LIMIT 10

DESC : descending order ( from newest to oldest ) LIMIT 10: first 10 records found.

This should do it :

$result = mysql_query("SELECT * FROM notes WHERE note_author_id='$u_id' ORDER BY date_time DESC LIMIT 0, 10");