To install Tweetdeck ( or any Adobe Air app) onto Ubuntu is pretty simple, thought of course it requires a few more steps than in Windows or OSX.
Install Adobe Air
1. Get the BINARY (.bin) file for Adobe Air. You can get it from:
http://www.adobe.com/products/air/
Make sure you get the .bin, as the .deb is built for 32-bit (i386) architecture.
2. Find where you downloaded the .bin, and give it execution permission:
chmod +x AdobeAIRInstaller.bin
3. Run the .bin
./AdobeAIRInstaller.bin
It will ask you a few setup questions, nothing too difficult. The defaults seem to work well for me.
Install Tweetdeck
1. Go to www.tweetdeck.com
2. Click on the "Download/Install" now. If everything went well during the AIR installation then it should magically all work.