Hi,
If you do not see Title bar on Art and Details window then right click on it and enable Title Bar (Move Window)

But how can I do it? Where are the buttons?

Yes just detach the art+details window.

I've got a bunch of music videos in my library. I'd like to run split screen with video playback on my tv, but still have the library accessible on the computer screen so I can edit the playlist while videos are playing. Is this possible, i.e., to run full screen videos in a separate window while retaining library access at the same time?