You should use Microsoft’s Xaml controls. If you create a “UserControl” like in the instructions I linked to you up above, you can then use Microsoft’s Visual Studio UI designer to drag-and-drop its Xaml TextBoxes and Buttons to your UserControl. Design a login window they you want it to look like to the end-user. I imagine you’ll want to create an OK and Cancel button. After dragging-and-dropping those buttons on to your UI, if you double click on a button in the UI designer, Visual Studio will automatically generate an OnClicked() method in your UserControl’s C# code that you can use to handle the button event. For the OK button, you should probably fetch text from your TextBoxes (user name and password), validate them, and then decide to send the login event to Lua or display an error message box to the user if something is wrong.
For error messages, you can use Microsoft’s built-in “System.Windows.MessageBox” class’ static Show() to display an error message to the end-user directly in C#. That’ll probably be easier than to set up the Lua/.NET communications to have Corona display a message box via its native.showAlert() Lua function. Just be warned that Microsoft’s message box is blocking (ie: rendering will stop) and you cannot customize the buttons (ie: limited to [OK] button… or [OK] [Cancel] buttons).
http://msdn.microsoft.com/en-us/library/system.windows.messagebox(v=vs.110).aspx
Alternatively, you can use Corona’s custom “CoronaLabs.Corona.WinRT.PhoneCoronaMessageBox” class which is what we use when you call our Lua native.showAlert() function. This message box works more like how you expect it to work on Android and iOS which is non-blocking and supports multiple custom buttons.