As @NaturalBornCamper said, mysql_insert_id is now deprecated and should not be used. The options are now to use either PDO or mysqli. NaturalBornCamper explained PDO in his answer, so I'll show how to do it with MySQLi (MySQL Improved) using mysqli_insert_id.
// First, connect to your database with the usual info...
$db = new mysqli($hostname, $username, $password, $databaseName);
// Let's assume we have a table called 'people' which has a column
// called 'people_id' which is the PK and is auto-incremented...
$db->query("INSERT INTO people (people_name) VALUES ('Mr. X')");
// We've now entered in a new row, which has automatically been
// given a new people_id. We can get it simply with:
$lastInsertedPeopleId = $db->insert_id;
// OR
$lastInsertedPeopleId = mysqli_insert_id($db);
Check out the PHP documentation for more examples: http://php.net/manual/en/mysqli.insert-id.php