Hi,
I am a Genius (only a job title, sadly not a term applicable to other aspects of my life) at an Apple Store in the UK.
From what you are describing, the image on your new screen is the same as the MacBook's, then your computer is "mirroring" the video signal.
There are several solutions.
Start by going to System Preferences (choose the Apple from the top left of your screen) and then click on the Displays icon. Choose the "Arrangement" tab and you can now select to disable the mirroring option. This will create an "extended desktop" allowing you to spread windows between both displays (like having one long display).
If you want to only use your big display as your main display you can drag the menu bar (little white rectangle) to your bigger display in the "Arrangement" tab.
If you don't want an extended desktop, plug in a USB keyboard and mouse, shut the lid on your MacBook and wait for it to go to sleep. Then hit a few keys on the keyboard to wake the MacBook and now your new big display is the only one which will display an image.
Hope this helps, and enjoy using your new display!
Regards,
Liam E.