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That done, you just need to click Start Steam to complete the installation. This will also download the latest updates to the Steam installer and client.
Next, you need to sign the Steam client license. For most of you this is a no-brainer. Hardcore free software users should keep in mind that the Steam client is proprietary software.
You may run into this error message. I did on both my Ubuntu 12.04 and 12.10, 32- and 64-bit respectively, desktops even though both had more than enough disk space. Just hit OK and continue on. This seems to be a harmless glitch.