Dear Irshad,
First you install the Microsoft SQL Server compatible to Microsoft Dynamics AX 2012 R3 (In my environment using the Microsoft SQL Server 2014 Standard edition) then install the Application Object Server (AOS) . And after successful installation of AOS Server with their required prerequisite .Net framework , Finally install the client application.
Click on the client application, if your installation mode of AOS Server and their setting will be in correct format then client application will open with Microsoft default entity (.dat) name.
Note: Before going to restore database you have to make sure the 'MicrosoftDynamicsAX' database should be in 'Single user mode' and also stop the AOS during the restoration time of DAX database.
After successfully restoration of database , start the AOS Server.
Before going to connect with your client application , first go to the 'System Administration' module . Go to Setup-> Checklists -> Initialization checklist.
Once the 'Compilation application' and then 'Compile into .NET Framework CIL' will be complete also verify the rest of the application checklist.
And finally connect with Microsoft Dynamics AX client application with AOS server.
The Microsoft Client application will connect with AOS server with your entity and all modules of the production environment will appear with in your test environment.
Hopefully it will help out to you.