Please note, this only seems to work for whichever desktop environment you are using when you install. If you install in Gnome and then try to run in KDE (or vice-versa) it may not work due to something with Air.
After much Googling and pain and suffering, I finally got TweetDeck working in my 64 bit install of Ubuntu.
If you use Twitter, have more than 20 or so followers and haven't tried TweetDeck yet, you don't know what you're missing out on. TweetDeck will help you organize the people you follow into groups, manage your direct messages, and even set up searches that watch the Twitter stream for certain topics. It's a must-have for anyone using Twitter on a regular basis.
I've used these instructions now in both Ubuntu 8.04 Hardy and 8.10 Ibex, and they worked well.
First, you'll want the getlibs package. (note, link updated 10/8/09)
"getlibs" will help solve the 32 bit library dependency problems. This is discussed on the Ubuntu forums. Install it by double-clicking the downloaded package.
It's easiest to do the rest from the console, so open a console and copy and paste the sections below and you'll be up and running in no time.
You'll need the following from the standard Ubuntu repositories. Enter the following in a console:
sudo apt-get install lib32asound2 lib32gcc1 lib32ncurses5 lib32stdc++6 lib32z1 libc6 libc6-i386 lib32nss-mdns
Next, use getlibs to install the following:
libnss3.so.1d libnssutil3.so.1d libsmime3.so.1d libssl3.so.1d libnspr4.so.0d libplc4.so.0d libplds4.so.0d libgnome-keyring.so libgnome-keyring.so.0 libgnome-keyring.so.0.1.1
The last three are specifically needed for TweetDeck and not Air.
To make it easy, just copy and paste the following into a console: (thanks go out to "mattgen88" for this tip)
sudo getlibs -l libnss3.so.1d libnssutil3.so.1d libsmime3.so.1d libssl3.so.1d libnspr4.so.0d libplc4.so.0d \ libplds4.so.0d libgnome-keyring.so libgnome-keyring.so.0 libgnome-keyring.so.0.1.1
The next one is suggested by a commenter below. I didn't find I needed it, but it may help some people out there. Air has put out an update since I wrote this guide, so it may be related to that. Anyway, if Air fails to work properly, try this:
sudo cp /usr/lib/libadobecertstore.so /usr/lib32
Download Adobe AIR. After it's downloaded, mark it as executable by right clicking on the file and choosing properties. Then, double-click it. You cannot use "sh AdobeAIRInstaller.bin" to run this.
After installing Adobe Air, I had to run the following from a console:
Finally, grab TweetDeck and use the Adobe Air installer on it.
Hopefully this will at least point someone else in the right direction.