This is a very relevant question, especially in today's learning environment where taking courses online is fairly common. The general problem is YouTube, forums, etc. are kind of like the wild west. Yes, there is great content out there and you can learn a ton. But there's no vetting process to upload videos or post content. There are also no standards that any of this content has to meet to be distributed to the masses. I think that's why the traditional education systems are still viewed as the most widely accepted methods of learning and demonstrating knowledge.

That being said, there are many websites that offer free, legitimate courses such as Coursera and MIT OpenCourseWare. These would be more acceptable to put on a resume, as long as you don't try to say "I went to MIT" or you took classes at MIT when in reality you just did a few courses.

I think the best way to quantify your self-study is to put the content or skills on your resume and say something like "Self-taught x subject through y number of hours". Even more powerful would be to include projects or successes you've had as a result of your self-study. Anybody can say they taught themselves something, but a proven track record can speak volumes.

I hope this helps. My background includes customizing resumes, successful interviewing and hiring, and proven strategies to increase your income. If you want to chat more about this, feel free to schedule a call with me and we'll go into more specifics on how to present these details in your resume.