I recently added a heading in my resume called personal work, under it I put stuff that I have taught myself, or have just learned over time, but that cannot be placed into an actual work environment.

As far as quantifying it, try not to learn things on sites that don't offer you some sort of proof that you actually did something.

I do a lot of learning on Udemy.com, they have a lot of free courses that are very well done, and can teach you a lot, and once you finish a course they give you a certificate of completion. At least that would give you a tangible proof that you took the course.