"the mysql extension is deprecated and will be removed in the future: use mysqli or pdo instead " Code Answer

the entire ext/mysql php extension, which provides all functions named with the prefix mysql_, was officially deprecated in php v5.5.0 and removed in php v7.
it was originally introduced in php v2.0 (november 1997) for mysql v3.20, and no new features have been added since 2006.  coupled with the lack of new features are difficulties in maintaining such old code amidst complex security vulnerabilities.
the manual has contained warnings against its use in new code since june 2011.

how can i fix it?

as the error message suggests, there are two other mysql extensions that you can consider: mysqli and pdo_mysql, either of which can be used instead of ext/mysql.  both have been in php core since v5.0, so if you're using a version that is throwing these deprecation errors then you can almost certainly just start using them right away—i.e. without any installation effort.
they differ slightly, but offer a number of advantages over the old extension including api support for transactions, stored procedures and prepared statements (thereby providing the best way to defeat sql injection attacks).  php developer ulf wendel has written a thorough comparison of the features.
hashphp.org has an excellent tutorial on migrating from ext/mysql to pdo.

i understand that it's possible to suppress deprecation errors by setting error_reporting in php.ini to exclude e_deprecated:
error_reporting = e_all ^ e_deprecated

what will happen if i do that?

yes, it is possible to suppress such error messages and continue using the old ext/mysql extension for the time being.  but you really shouldn't do this—this is a final warning from the developers that the extension may not be bundled with future versions of php (indeed, as already mentioned, it has been removed from php v7).  instead, you should take this opportunity to migrate your application now, before it's too late.
note also that this technique will suppress all e_deprecated messages, not just those to do with the ext/mysql extension: therefore you may be unaware of other upcoming changes to php that would affect your application code.  it is, of course, possible to only suppress errors that arise on the expression at issue by using php's error control operator—i.e. prepending the relevant line with @—however this will suppress all errors raised by that expression, not just e_deprecated ones.


consider whether you really need to upgrade to php v5.5 at this time.

you should begin planning to replace ext/mysql with one of the other, more modern, extensions in order that you can reap the rewards of the benefits they offer; you might also use it as an opportunity to refactor your database access methods into a more modular structure.
however, if you have an urgent need to upgrade php right away, you might consider suppressing deprecation errors for the time being: but first be sure to identify any other deprecation errors that are also being thrown.

you are using a third party project that depends upon ext/mysql.
consider whether you really need to upgrade to php v5.5 at this time.
check whether the developer has released any fixes, workarounds or guidance in relation to this specific issue; or, if not, pressure them to do so by bringing this matter to their attention.  if you have an urgent need to upgrade php right away, you might consider suppressing deprecation errors for the time being: but first be sure to identify any other deprecation errors that are also being thrown.
it is absolutely essential to perform regression testing.

<?php
$db = new PDO('mysql:host=localhost;dbname=testdb;charset=utf8', 'username', 'password');
$result = $db->exec("INSERT INTO table(firstname, lastname) VAULES('John', 'Doe')");
$insertId = $db->lastInsertId();
?>
A basic example of using MySQLi (without error handling):
$db = new mysqli($DBServer, $DBUser, $DBPass, $DBName);
$result = $db->query("INSERT INTO table(firstname, lastname) VAULES('John', 'Doe')");