What are some intuitive ways to think about one-relator groups?
I am aware of the Freiheitsatz, and Bass-Serre theory. What I'm interested in are ways people who work extensively with one-relator groups think about them. I'd like some help with the intuition.
To elaborate a bit more: Are there diagrammatic tools to study these? What are the go-to rewriting procedures? What is an intuitive description of the realization of these as HNN extensions (as found in Lyndon and Schupp, for example). What are the go-to techniques and tools in the modern viewpoint? Although I'm aware of the Freiheitsatz and Bass-Serre theory, an expert description of how these are employed to study one-relator groups wouldn't be off topic.
Thanks in advance!