Edge templates everybody should know
In all the diagrams, Red is the vertical player and wants to connect her stone or stones to the bottom. Unshaded cells are part of the carrier of each template and must be empty for the template to be valid. Shaded cells are not part of the template and can be occupied by Blue.
What players "should" know if of course a bit subjective. The more templates you know, the better. But the ones shown on this page are quite common and are a good start.