I think the first thing that will help is an explanation of the difference between cloud computing and "good old VPS!"
A VPS is a managed machine setup specifically for web hosting. All the niceties you get are pre-configured Apache, tested versions of PHP, set amount of space, a nice control panel, etc. You don't have to worry about configuring or managing the server, that's all done for you.
Cloud computing is different, it's like picking up a new server and plugging it in for the first time. Nothing is pre-configured or managed for you but you have the power and flexibility to set it up however you like.
So to run a php script, you'd need to launch and configure an instance to run your web server of choice and also add PHP support. This is usually pretty straight-forward using the built-in package manager on your distro of choice (apt for Debian/Ubuntu and yum for CentOS/Fedora). We do have some instructions in our wiki for those - http://wiki.dreamhost.com/DreamCompute
If you're looking to use DreamObjects in your app, it would be no different if it were running on a VPS or a DreamCompute instance. The data in DreamObjects is accessible via URL so you'd just link to them appropriately.
It's hard to offer anything specific to your particular situation but hopefully this information is helpful as a starting point.