The answer to your question is the following:
Utilize the mysqli API as opposed to the mysql API
http://us1.php.net/mysqli
There is a bit of learning involved because the functions don't behave exactly the same, but it's for the better.
For example, instead of using mysql_connect() to get your connection you would use http://us1.php.net/manual/en/mysqli.construct.php
Additionally, please follow these steps to make sure you have access to mysqli and PDO, as it's going to vary based on how you installed php
http://us1.php.net/manual/en/mysqli.installation.php
So, in summary, what that post you've pointed out is saying is that functions starting with mysql_ are deprecated and to not use them anymore.