Oscar, your question is so interesting that I’m interrupting my Valentines Day dinner with my wife to reply. “How do I go about doing something?” means the same as “How do I do it” PLUS “I really don’t know how to do it”. So it is a question plus an admission of ignorance.

Great question: "Go about.." doing something is to start doing something and then making some progress on it. OR to deal with something like solving a problem, creating something, navigating a situation. (as a spanish student i was told it was similar to using ANDAR + verbo gerundio) 'How do I do in order to have a good idea?' - this sentence is wrong. You could say "what" instead of "how"...but that is a slightly different meaning. What do I do is very to the point, a specific action. "go about doing" is more fluid and progressive and cumulative.

It’s common and in use. There are many good answers already, but I don’t think that your example is a good example, because ‘getting a good idea’ isn’t something that’s easily describable. The idea of ‘going about doing something’ is that the process might be long and complicated. You aren’t looking for a short answer and are open to hearing a long description. You’re the expert in this field. How would I go about getting certified for this tool? (Learn to use the tool doing x, practice doing y, arrange a certification test with person z etc.) Asking it suggests a genuine interest on your part. How does one go about getting a work permit if you’re not from the EU? Ask Jim how to go about finding a language partner.