How to convert a single vertex into a plane within a mesh? I've seen two different videos where the user selected a single vertex and then expanded it into a 4 sided plane. This is a technique I've needed many times but I am not sure how that was accomplished.

This picture sort of demonstrates what I'm trying to reproduce. 
before (left) and after (right)
Select the vertex and press CtrlShiftB that will bevel the vertex, creating a new face.
Do note that doing so will create Ngons in the surrounding faces.