Well, the best way to handle db connections regardless of how many is to use an abstraction layer like PEAR:😃B, you can then create multiple instances and use them throughout. However, if the word "abstraction layer" threw you for a loop then forget that for now.
The standard way would to just create multiple handles and the most direct answer to your question would be:
$myConn = mysql_connect( parameters );
$myConn2 = mysql_connect( parameters );
You can then use these with your mysql_query() statements accordingly.
In the future, you should look into using abstraction layers (object oriented libraries) that have been written by the PHP community in the future. http://www.zend.com and this site have a few articles on their use and http://pear.php.net is the home of a few of the more robust DB abstraction layers.
