If you don't know if it runs locally means in most cases that it does run locally.
The normal way to startup KDE from a console is
startx /path/to/kde/bin/startkde. I tried to run startkde from another wm, and (althought it works partially) kde appears as windows in my previous wm.
You can (in most configurations) open two x-sessions. You can open a new KDE-session with the following command:
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Source code
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1
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startx /path/to/kde/bin/startkde -- :1
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Afterwards, you can switch between those sessions with
Ctrl+Alt+Fn where Fn is (in my case) F7 and F8, but it depends on your distribution.