Hi fl401,
The Apple TV connects to your existing wireless internet connection, so it works in conjunction with your existing router. It is physically connected to your TV via the HDMI port. It gets its power from the cord plugged into an electrical outlet.
The newest version is the Apple TV 4. I'll include the User Guide below so that you can see the setup diagram and see all of its features.
http://help.apple.com/appletv/
To use Apple TV, you need:
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A high-definition TV with HDMI capable of displaying 720p or 1080p video
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An HDMI cable to connect Apple TV to your TV
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Access to an 802.11 wireless network (wireless streaming requires 802.11a, g, n, or ac), Ethernet network, or broadband Internet
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An iTunes Store account for iTunes purchasing, renting, and using Home Sharing
Set up Apple TV. Before you start, make sure you know your wireless network name (and password if the network is password-protected). If you’re using a wired network, use an Ethernet cable to connect your Apple TV.
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Connect Apple TV: Connect one end of an HDMI cable to the HDMI port on your Apple TV, then connect the other end to the HDMI port on your TV.
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Plug in Apple TV: Connect one end of the power cord to the power port on your Apple TV and the other end to a power outlet.
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Select the HDMI input on your TV: Turn on your TV, then select the HDMI input that’s connected to your Apple TV. On some televisions, this may occur automatically.
Happy Holidays!