I don't know how else to say it so I'm just going to explain my ideal scenario and hopefully you can explain to me how to implement it...

I'm creating an application with the Zend Framework that will be hosted with DreamHost. The application will be hosted on its own domain (i.e. example-app.com). Basically, a user should be able to sign up, get their own domain sampleuser.example-app.com or example-app.com/sampleuser which points to, what looks like their own instance of the app, which is really a single instance serving up different content based on the url.

Eventually, I want my users to be able to create their own domain (like foobar.com) that points to sampleuser.example-app.com, such that visitors to foobar.com don't notice that the site is really being served up from example-app.com.

I don't know how to do most of that stuff. How does this process work? Do I need to do some funky stuff with Apache or can this be done with a third party host, like DreamHost?

Update: Thanks for the advice! I've decided to bite the bullet and upgrade my hosting plan to utilize wildcard subdomains. It's cheaper than I was expecting! I also found out about domain reseller programs, like opensrs.com, that have their own API. I think using one of these APIs will be the solution to my domain registration issue.