If the application is using the Razor view engine (.cshtml files) you can use the following inside your view/layout to display the controller and action names:
@ViewContext.RouteData.Values["controller"].ToString()
@ViewContext.RouteData.Values["action"].ToString()
If it is using the WebForms view engine (.aspx files) you can do something similar with:
<%= RouteData.Values["controller"]%>
<%= RouteData.Values["action"]%>
The controller class will usually be named as in the route data plus "Controller". The action names will usually match a method name in the controller.
You may also consider getting a branch of the project just for you, and then install glimpse via Nuget. That may help you understand better the application.