There's two parts to the process.
Step #1 - You'll need a MiniDisplay Port to HDMI adapter (with or without audio)
The audio integration is preferred, otherwise you'll need a 2nd cable for audio from the computer to the TV.
Step #2 - An HDMI cable to run from the adapter to your TV, the length of that cable will depend on how far your computer is from the TV.
To clarify all:-
You identify the port on your Macbook Air first.
Then identify the inputs on your TV/Display:-
- PC/Monitor (15 pin D connector)
Apple Stores (and others) sell cables that can be used to interface the two but you need to be aware of some things. If you use the monitor cable, unless you have the extra audio jack alongside the D connector then you need a separate audio cable to go from your headphone socket to the TV to output the sound on the TV.
For my PC laptop, I have two cables (video and audio) to connect to the PC port on my LCD TV but my macbook air uses the Apple one that interfaces to one of the HDMI ports.
You wil have to experiment to identify which AV port you are using and want to use of the TV once the two are connected up.