I think once you understand the graph, then looking at what the graph looks like and what you want it to look like usually leads you to being able to figure out what operation you want.

And then git fetch/push/pull are mostly about copying parts of that graph from one place to another.

After that, it's mostly a question of what workflow you want and that becomes much more than a git question because git works for a variety of workflows, and many of the features of git are really only relevant for certain flows.