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At this point, you'll have the Steam client installed. From here you'll need to either create a new Steam account or sign into your existing account. If you an account on another operating system it will work fine here too. Just keep in mind that not all the games you currently have on your other systems work yet on Linux.
Once you've logged into Valve Software's Steam server you'll see your Steam game library for Linux. This display will be empty until you've downloaded some Linux-compliant Steam games.
So the next thing you should do is to head to the Steam Store and look for games to download and play.