How to make a first-person style game with arrow key movement?

You need a virtual camera to achieve what you intend if you are not using stage3D.

Here is a basic switch usage to move something with the keyboard:

stage.addEventListener(KeyboardEvent.KEY_DOWN, move_mc);

function move_mc(event:KeyboardEvent):void {
    switch(event.keyCode)
    {
       case  Keyboard.LEFT : mc.x -= 5
       break;
 
       case  Keyboard.RIGHT : mc.x += 5
       break;
 
       case Keyboard.UP : mc.y -= 5
       break;
 
       case Keyboard.DOWN : mc.y += 5
       break;
    }
}