They make lengths of cat cable, it's no more complicated than plugging in a phone. The biggest issue is running the cable from the router to the device.
As far as the wireless goes our TV has connector in the back specifically for the wireless, looks like it's proprietary port and the adapter is bought separately.
You can buy a wireless bridge like this assuming you already have a wireless router. This particular model uses a USB port on the TV for power so that would be one less plug.
NETGEAR - Universal Wi-Fi Wireless-N USB Adapter - WNCE2001-100NAS
I'm not recommending that model, it's just an example.
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Just to add our Home Theatre has wirless adapter included. You'd have to check to see if your TV has one included.