How do I install steam on a 64bit system?

Alright so my computer is 64-bit and I only want to use Linux to install Steam, play Team Fortress 2 and get that penguin item but It's not working out for me. The version of Ubuntu I installed was the "Wubi.exe" which let's me use it along with Windows. But when I get it up and download the Steam .deb file, it tells me "Wrong Architecture 'i386'". What do I have to do to run Ubuntu alongside windows without using a CD/USB stick?

Open the terminal and type:

sudo dpkg --add-architecture i386
sudo apt-get update

Try installing it after doing that.

For future reference look: https://wiki.ubuntu.com/MultiarchSpec & https://help.ubuntu.com/community/MultiArch

EDIT [Preferred Method on new Ubuntu]

As of Ubuntu 16.04 you can now do the following:

$ sudo add-apt-repository multiverse
$ sudo apt-get install steam

OLD ANSWER:

Try installing the ia32 libs by opening up a terminal and entering the following:

$ sudo dpkg --add-architecture i386
$ sudo apt-get update
$ sudo apt-get install ia32-libs

Once that has run and installed, then use terminal to install Steam for you. Run the following in terminal:

$ sudo apt-get install steam

Now you will have Steam installed and you should be able to launch it as expected.

sudo dpkg --add-architecture i386
sudo apt-get update
sudo apt-get install lib32z1 lib32ncurses5 lib32bz2-1.0
sudo apt-get install steam

it's working with Ubuntu 14.04 LTS on iMac 2008 via Dual-boot with rEFInd.