Customer Domain "appear Everything From Subdirectory" To A Multi Customer Application

I'm not really sure where to start with this and therefore can't pick a more specific area to post. At first I though this might be something I would do in IIS7 but on reflection i think it needs to be at the application level. I am developing an application which will as part of it's function provide a unique website (custom CMS) to my customers. Each person who registers will have their own site accessible via a url such as [URL]. I need someway to take this and work out which customer it is and then load the rest of the pages with their content. So the site may have a home, about us and news pages for example and be themed to the customers requirements. Each of the pages will be the same aspx file and application for all customers but the content and style will be loaded from the database at runtime. I'd like for the duration of the visit for everything to appear as if from this subdirectory without actually creating them for each customer. so thy could visit [URL] but it actually loads [URL] and loads the content based on the customer site the visit is viewing.

I'm not really sure how to approach this. Maybe using a session value to store the customerid for the site the person is viewing which could be calculated from the URL on the first visit. I presume other people have done something simialr in the past. Where it gets more complex is if I then want to offer customers to have there own domain name pointed to the site. In that scenario they would have say [URL] which points to my server and bound to my application [URL]. All pages would have look as though they were on the customer website such as [URL] but still point to [URL] in the background and also somehow link to the customerid in the database to load the correct content.