How can I make it possible for users to use the \'\"\' (double quote) inside a textfield...
Whenever I do use double-quote in the field (the value) then when receiving t
You have to use htmlspecialchars($str, ENT_QUOTES) or htmlentities($str, ENT_QUOTES) to convert the quotes to the HTML entity ". Those function also take care of other characters that should be encoded.
mysql_real_escape_string() is only meant for escaping single quotes in database queries, so that you can correctly enter strings with single quotes into your database (and avoid SQL injections).
EDIT: Added parameters. Thanks to micahwittman