It's pretty simple if you get away from the idea of "pointing to folders" or configuring Apache individually for each site. Just configure Apache to direct all requests to a specific application/PHP file/folder/whathaveyou. In that application, check the HTTP Host
request header to get the requested domain. Then do anything with it you want. This can even be done using simple rewrite rules in Apache instead of some full-blown application, depends on your needs.
You'll just have to instruct your users to configure their DNS server for their domain to point to your IP address.