I have tried a couple of different methods of installing Steam.
If I install "Steam Installer" by searching for Steam in the software centre, and click launch, nothing happens.
If I try to install it using the command line, using these instructions, when I enter "gdebi steam.deb" it outputs "gdebi error, file not found: steam.deb".
If I try to download Steam directly from Valve here, it opens the software centre, and as with installing from the installer in my first method, nothing happens when I click install.
Best Answer
sudo apt-get install gdebi
When prompted select "Other" and then select "GDebi" as the installer as shown below:
Click "Install Package", and when you see the image below click "Start Steam" to complete the installation.
Enjoy!
Edit: For some reason I had to run
~/.local/share/Steam/ubuntu12_32/steam
to get it to launch and update the first time. Since then it launches normally.