Steam is made specifically for Ubuntu 12.04 32-bit. I run Xubuntu 12.04 64-bit, so after reading a few sites, I finally got things working properly. From here, I’m assuming you’ve already installed Xubuntu and the proprietary driver for your video card.

1) Snag the 32-bit version of Flash from Adobe. Mine defaults to 64-bit Linux, so I had to select the different operating system option at the top of the page. Select the 32-bit, .tar.gz package and download that.

2) Extract the tarball, and copy into the /usr/lib/browser-plugins
From a terminal window
cd ~/Downloads
tar -xvzf install_flash_player*
sudo mkdir /usr/lib/browser-plugins
sudo cp libflashplayer.so /usr/lib/browser-plugins

3) Install 32-bit libraries
sudo apt-get install ia32-libs -f
sudo apt-get -f install

4) Download and install Steam
wget http://repo.steampowered.com/steam/archive/precise/steam_latest.deb
sudo dpkg -i steam_latest.deb

Sources:
32-bit Flash fix
32-bit Library — comment from Alejandro

Steam is finally available on Linux.

Hazzah!

http://steamcommunity.com/games/221410/announcements/detail/1747660173332716773