How do I eject an memory card reader from a MacBook Air?

You don't need to eject an empty memory card reader. You eject the volumes corresponding to the memory cards themselves.

If you go to Finder > Settings… in the Finder, you will find checkboxes for "External disks" in the General and Sidebar tabs. You will probably want to check both boxes so that memory cards show up as icons on the Desktop and show up in the list of Locations in the sidebars of Finder windows.