Which MacBook Air do you have?
Of the older ones with the MagSafe connector to charge them, the 11" version has a single Thunderbolt 2 port and the 13" version has two Thunderbolt 2 ports and an HDMI port. You should therefore be able to connect either of these with a "Mini Display Port to HDMI" cable or, in the case of the 13" version with an HDMI cable.
The more recent MacBook Airs have USB-C / Thunderbolt 3 ports and you would use a USB-C to HDMI cable. The necessary settings are to be found in "Displays" in the Settings app. There shouldn't be anything to configure other than perhaps the resolution. Obviously in the TV you need to select the relevant HDMI input.