I’m new to Blender, just started learning it for a week already with the help of a guide book.
As per the instruction in the guide book, I tried right clicking on the (A) vertex and Ctrl LMB on a point just above (A) in attempt to create a new vertex but nothing happened. I haven’t got no problem earlier creating vertex (A) though. Did I miss anything out there? Your kind assistance is much appreciated.
(Shift-D - move mouse - click somewhere) duplicates the vertex and places it where you click.
F creates an edge between two selected vertices. Or fills in a face between 3 or more vertices (or edges).
E extrudes the edge to a face…
Looks as if your last operation was select shortest path which is Ctrl+RMB by default. Either you used that, or have switched select button order in preferences and might not be able to use ctrl+LMB for quick extrusion.