You're asking the wrong question. The how is easy: build a blog (trivial) and write down the things you've learned. Maybe add some pictures, diagrams, or code.

You're asking the wrong question. The how is easy: build a blog (trivial) and write down the things you've learned. Maybe add some pictures, diagrams, or code. You really are wondering why you should blog. There's nothing wrong with sounding academic. In fact, being able to teach others is perhaps the best way to solidify your own understanding. At any point you use jargon, define the term! If something seems confusing or esoteric to others (via comments), answer the comments and use that to generate ideas for follow-up posts. Can you talk about this stuff legally? Legally yes+, you're not plagiarizing any existing works since this is your own original writing. Better, you want to know what's in your school's code of conduct. It's probably not a good idea to list answers to homework problems (unless they are from a book and the book has the answers in the back). But it's good to explain the concepts as well as how you might go about solving it or thinking about it. + = I say this not as a lawyer, and I am not giving you legal advice