Hi, James!
I guess the best way would be to place a CBrowser (don't remember the correct name)-derived component on the dialog and just open the URL through it. This is not that much work. Examples are everywhere on the net, I think Microsoft even has examples on making a custom browser using this component (for MFC).
As to talking to a PHP script directly on the same machine (in case you want to do this), I think this is not a very good idea because you would need to ship PHP and install it on the client's computer. But if you need to connect to a particular site, it will be a snap.
If you don't use MFC, you would need to check whether IE is installed on the machine and then use CreateWindowEx to create a IE window on your dialog.
Best regards,
Stas