You use the Time Machine Restore application that is in your Dock to retrieve content from your Time Machine backup drive.
In the Finder, dragging and dropping files in your user account will move them. Pressing the option key will present a green plus symbol indicating a copy operation.
Alternatively, and perhaps confusingly, you can select a file/folder icon, and then control/right-click. From the pop-up menu, choose copy. Then click at the destination where you want the file object placed, and if you just want to copy it there, then choose Paste Item. If you want to move it, press the option key, and choose Move Item Here.
And a third option is to use command+C to copy the file object, and command+V to copy it at the new location. To move it, same command+C to copy, and then option+command+V to move it.