first: you could try to access your databse directly (eg. mysql_connect("http://www.blah.com"); ). But that's in most cases restricted.

so you better do it this way:
write a simple php-routine and put it on the server where your database is running. Select all data you want to display on the other one and just echo them so that you get a plain text.
On the other server you can get these data with pfsockopen (http://de3.php.net/manual/en/function.pfsockopen.php).
For security you can have a simple password that you send via HTTP (a bit unsave though). If it's not enough then crypt it with MD5 or RSA (see wikipedia).

One more thing: pfsockopen is also restricted on some server. So try it out before you do all the fuss with coding.