如何使用不同的URL的所有相同的类实例？

Twitter and facebook, among others, display the same page layout and then they fill it with specific information based on url information.

For example: twitter.com/bob will show the profile layout/page but with bob information.

Using a standard URL structure (domain.com/controller/action), how do I call the same controller with a different url each time?

Just add an additonal route when you have

/{controller}/{action}

you can also add

/alias/{action}

you just need to pass it to the desired controller instead of the variable used in the default route

You need three things.

1. A web server that allows for URL rewriting such as Apache with mod_rewrite or Nginx with a proxy setup.
2. A Front Controller
3. A router that will map the URLs

Front controllers are simple scrips where all of your requests get routed to. This will usually instantiate the router & other objects. The router is what takes care to instantiate the controller & pass it parameter from either the query string or the POST body or the URL.

You should look at Slim or Aura for router implementation examples.