The HomePage in Orchard up to 1.3 is managed by IHomePageProvider, but the interface is a bit strange and it's about to disappear completely in Orchard 1.4 so I'd advise against it.
However you can just create a Controller and then implement an IRouteProvider to route the home page to your controller. This is how all paths work in MVC / Orchard including the home page. So just set a route with a higher priority than the existing homepage
and you're set.
From your controller you can then output whatever content as your logic, and how to do that depends what type of content it is.
The IRouteProvider for the existing homepage is in Core\HomePage\Routes.cs.