There is 2 ways you can do this, depending on what you have available to you at the time of saving.
If you have the data that was already in the field available in a variable, then best to just use PHP to append the addition to the string.
or you can use the SQL function CONCAT() to do it for you
UPDATE myTable SET message=CONCAT(message, '$newMessage') WHERE id=$myMessageID
as for adding a timestamp or newline you can use sprintf()
$newMessage = sprintf("\n%s - %s", date("d/m/Y"), $form_newMessage);
might check syntax, writing from memory and before bed ;)
anyway, hope this helps you.