Hi, Mark -
It is not clear to me where to find the closed System Folder icon to drop this thing into,...
That refers to the System Folder itself, which should be visible when the icon of the hard drive is opened - it is a folder with the name System Folder.
The icon of any drive or folder can be closed or open. A drive or a folder is opened by double-clicking its icon - when opened, there will be a window displaying its contents. To view the contents of a drive, double-click its icon - all drive icons are shown on the right-hand side of the desktop; by default, the icon for the boot drive will be the topmost one in that column (its default name for the original drive would have been Macintosh HD, but many folk rename their drives).
To drop an item into a closed folder, close all windows for that folder; drag the item onto the icon for that folder; when the folder's icon darkens ('highlights'), let go of the item.
...and I don't know where the Extensions folder is either.
The Extensions folder is located inside the System Folder - double-click the icon of the System Folder to open it, and you will see an array of its contents; among the items will be a folder named Extensions. That array will be in either icon view or list view, depending on how the view has been set for that folder. View as List makes finding things a lot easier in a folder with many items; you can change the view setting for any folder's content by opening it, then selecting the view preference in the View menu.
(Is it the same as the Extension Manager in the control panel?)
No. Extensions Manager is a control panel. Extensions is a folder. Extensions Manager uses the Extensions folder, along with its companion folder Extensions (disabled), to control which extensions are to be active and which are not.