First off, I was seriously unhappy with Ubuntu 13.10. What a mess… Now that that is out of the way, it makes sense why I just reverted to a clean install of Ubuntu 12.04 x64 (LTS). I was using Valve's Steam on my 13.04 box before the 13.10 debacle just fine, but I ran into issues starting up Steam on 12.04. Turns out there were a bunch of missing libraries that it needs. The good thing is, it's an easy fix!

Before downloading the client, it will need curl to bootstrap itself:

sudo apt-get install curl

There are going to be a bunch of libraries you need to install for Steam. Just run the following (this is on an x86_64 install, so if you are using an i386 install, you can drop the :i386 part):

sudo apt-get install fontconfig:i386 libfreetype6:i386 \
    libavahi-gobject0:i386 libgtk2.0-0:i386 libopenal1:i386 \
    libsm6:i386

It probably doesn't hurt to also install the ia32-libs meta package:

sudo apt-get install ia32-libs

That should suck in just about anything you could need.

Next, just download the latest steam client and run:

sudo dpkg -i ~/Downloads/steam_latest.deb

That will install the bare bones latest stuff, which will actually download the client. It should just work now. If not, try running it from the command-line using the steam command and check the output.

Getting the list of missing shared libraries was how I figured this out. Valve does have a helper page up here that will get you going if you know a good amount about Linux.