Well, I don't know if this is the best way, but I connect using this code:
// Now into the MySQL. Open the database
$db = mysql_connect( $host, $username, $dbpword );
$connection = mysql_select_db( $database, $db );
As for displaying results, you can use the functions mysql_fetch_row(), mysql_fetch_array(), or mysql_fetch_object(). Each one is slightly different, but my favorite is mysql_fetch_object(). 🙂