The television we have supports the use of the internet through an Ethernet cable or wireless USB network adapter (bought separately). The television has no built-in wireless and the nearest ethernet port in the house is too far away to be practical.
You should be able to do this via Ethernet or wireless, depending on whether you want to buy a wireless dongle for your TV or whether you have the Ethernet adapter for your MacBook Air.
General instructions from Apple support:
Either approach should work - it's most likely a matter of the hardware that you have (or are willing to acquire). Getting the USB Ethernet adapter for your MacBook Air is likely to be cheaper (and of more use long-term) than a dongle for the TV.