How can I make the documentation pop-up on hover in PyCharm?

If you are stopped at a breakpoint, PyCharm doesn't show quick documentation on hover even when the box is checked, because it is in "inspect variable on hover" mode. In that case, hold down Cmd while you hover (on a Mac).

When Settings | Editor | General | Show quick doc on mouse move is checked already, look for a window Documentation, which be explicitly opened with Edit | Quick Documentation.

I had barely noticed that window, but quick doc may show up in there. Instead, to show the doc hovered near the mouse, right-click on the header of the Documentation tool window and select Open as popup.