Finally, starting today, Valve has released Steam, a popular video game store for the PC for all Linux users. The client itself is still in beta, however. So if you run into bugs don't be surprised, but it should be at least a bit stable, but not stable to a fault, I would assume. Otherwise it would have dropped "beta" out of it's name already.
The Steam website also added a Linux section where you can browse for Linux compatible games, and of course grab the client to install on your machine. The Steam client right now is a simple .deb package that you can install via the Ubuntu Software Center, or my favorite package-installing app GDEBI, if you have that installed. Either way click open the file and click install :)
Ubuntu has a nice wiki page on installing Steam, and they even have an IRC channel specifically for Steam, which is #ubuntu-steam on Freenode. They recommend you run the most update drivers for your graphics card. Those are the beta drivers, but you can choose to install more updated but not deemed stable yet drivers or not. If you are running Ubuntu 12.10 you shouldn't have issues or extra steps, but it's a good idea to read that page anyways.
What to download the Steam client? A nice button is waiting for you below...