To duplicate / copy a project and it's tasks click on the Info icon next to the project title either on the dashboard or on your project board.
Now click on … at the top right of the project dialog and click on Duplicate...
You are then able to set a title and description for your duplicated project and to select what you want to duplicate:
Click on Continue to duplicate the project.
That's it, you are now able to duplicate projects and can even use them as templates.