This was actually pretty simple, you can either download the installer through your web browser or use wget to retrieve the file at:
chmod +x AdobeAIRInstaller.bin
Then install the application using:
Once the application is installed it will auto-update to the latest version (2.0 at the time of writing). With the auto-update complete you can now install TweetDeck by going to http://www.tweetdeck.com/desktop/ and clicking the “Download now, it’s free” button. The .air file should then be downloaded and installed automatically, this took 2-3 minutes on my netbook.
If everything worked correctly then TweetDeck should start up once it has installed