These are few steps to get Steam running on Ubuntu:

wget -c media.steampowered.com/client/installer/steam.deb
dpkg -i steam.deb
apt-get install -f
apt-get update

Solutions for some issues

Some time ago I needed 32 bit flash even on 64 bit system - I don’t need it currently but I’m living this as a tip.

apt-get install adobe-flashplugin:i386

After Ubuntu upgrade I was unable to run Steam anymore - It shouted on me with strange “networking problem”. I have to clean Steam configuration with:

steam --reset
Sources

http://linuxg.net/how-to-install-the-latest-steam-client-available-on-ubuntu-13-10-13-04-12-10-12-04-and-linux-mint-15-14-13/external link
http://askubuntu.com/questions/353522/why-is-steam-not-able-to-connect-steam-networkexternal link