How can I determine what version of PowerShell is installed on a computer, and indeed if it is installed at all?
Use $PSVersionTable.PSVersion to determine the engine version. If the variable does not exist, it is safe to assume the engine is version 1.0.
Note that $Host.Version and (Get-Host).Version are not reliable - they reflect the version of the host only, not the engine. PowerGUI, PowerShellPLUS, etc. are all hosting applications, and they will set the host's version to reflect their product version — which is entirely correct, but not what you're looking for.
PS C:> $PSVersionTable.PSVersion
Major Minor Build Revision
----- ----- ----- --------
4 0 -1 -1 