You don't have to connect to a TV, but then all contestants must huddle around the iPad to see the game board and read the questions as they are presented. So this instruction is for connecting to a TV. Skip it otherwise, as the rest of the directions are pretty much the same.
If you are connecting to a TV using Apple's 30-pin to HDMI adapter, plug the cable in to both the iPad and the TV. On your TV select the appropriate HDMI input.
If you are connecting to a TV using an AppleTV that is already set up set your TV to the input for your AppleTV. Double-tap the home button on your iPad and scroll to the left end of the multitasking bar, which reveals the AirPlay button (a hollow rectangle with a triangle on the bottom of the rectangle). Tap the AirPlay button to present the AirPlay picker, and tap the list item that corresponds to your Apple TV. Doing so should expand the list to include a line item "Mirroring" with an on/off toggle. You want that toggle to be in the "On" position.
Once the connection is made, open Guess & Know on your iPad, if you haven't already. You should a short intro movie appear on the screen, followed by a notice that a game is about to start. These serve as confirmation that Guess & Know has noticed the addition of the TV screen into the game.