While there is no absolute dividing line between formal and self-education, it seems obvious that in highly technical skill areas you are best advised to learn through formal, well-conceived educational programs usually in the best universities you are able to attend. Clearly, if you need a string of degrees to qualify yourself as a chemist or a mathematician, you may get a start by self-educating your way through some fundamentals, but in the end, you will need to learn many important concepts under the guidance of professionals who know or practice the field at a high level. In these areas and others where one must go through a kind of apprentice training requiring that one learn under the one on one guidance of a mentor, the idea of doing that as self-education seems unrealistic. There are certainly elements of self-education, but an apprentice must be certified as having learned what is necessary from a mentor.
There are times when you can learn significantly about an area of human inquiry entirely on your own. The approaches are variable and certainly not one-size-fits-all. I think it is best to simply start reading widely about an area of interest, and without too much discrimination at the outset. Read as much as you can without deciding what’s a really good analysis or perspective, compared with what might not be so good, off the mark, or just sketchy. You can start by googling the subject on the internet, or going to the local library. Many writers of articles or books will know much more about the subject than you do, and you’ll need to reflect a bit and let some of that knowledge sink in. You may have been surprised to learn just how much has been written.
You will certainly find that many others have thought seriously about the subject of interest all along. Some may have a clear perspective, but others may not. Some will think about the area comprehensively while others will only take on a small piece of it. None of that matters too much at this early stage of your inquiry. Just keep reading, making notes on what the major issues are, what points keep coming up again and again, what matters are settled and what matters have provoked argument or at least heated discussion. Make detailed notes–think about things.
Perhaps you want to keep separate notes on parts of the subject where you believe there may be room for new views, where suggestions of rethinking some matters not effectively considered might be welcome–at least it may be time for a second look.
Early on in your reading program you want to set some goals, collect materials, start making connections between what appear to be the most important contributors to the field. Work up an outline identifying key works you’ve read and organize within that context other works that may be secondary to the major ones. Clearly, you’ll be finding that many others know much more about the subject than you do.
Don’t let yourself be intimidated by the knowledge of others. The self-knowledge you are developing may be just for your own self improvement. However, if your learning about a field of knowledge new to you with the idea of becoming a “mover and a shaker” in that area, then clearly you’ve got some additional work to do.
When you have decided what’s important, what the key issues are, and what’s secondary, write about the subject based on how you currently understand it. Plan on writing somewhere between 10 and 30 short essays, between 250-1500 words each. Don’t try to do this in a hurry. Pick low hanging fruit first. Think out more advanced ideas and perspectives as you go along. Write out a few paragraphs or an outline of the subject you want to tackle in tomorrow’s essay today, then tomorrow morning read it through and add a few ideas you may have missed before you actually start writing.
Write a few essays and then take a look at your comprehensive list of topics and revise the list or break up topics for later essays. Come back after you have finished, reread your essays in the order you produced them. Decide overall what the most important issues are and write additional essays on subtopics you missed, but which you feel are important enough to include at this stage. Throughout, if you have quoted any one make sure you have quotation marks in appropriate places, if you are repeating someone’s idea, be sure you give them credit even if you are only paraphrasing the idea.
Once you have finished these essays, you’ll want to evaluate if you’ve left out anything that is key to your overall understanding. Double check any logical analyses or mathematical ideas even if they are only noted as conclusions in the essays. Then give everything a month to cool off. Go to the beach or read and think about something else. Then, return and re-read everything you wrote and decide where you are taking your knowledge. Do you want to read more? Double check some of your analyses that may seem weak. Decide what you want to do next.