I have some code that I want to put on Stack Overflow for a code review. What is the best way to handle multiple files? Should I just ask a question and put a link to a public GitHub repository? What do people usually do in this case?
Stack Overflow is better suited for practical programming questions about specific issues. Try CodeReview.StackExchange.com for code reviews. Be sure to read their FAQ though. For one, I think it's preferred or even required to put your code (the relevant bits) in the question to make it stand on itself, as well as to prevent link rot. To quote the relevant bits from their FAQ:
What topics can I ask about here?
Code Review Stack Exchange is for sharing code from projects you are working on for peer review.
Make sure you include your code in your question
This site is for code reviews, which are hard to do when the code is behind a link somewhere out there on the internet. If you want a code review, you must post the relevant snippets of code in your question. It is fine to post a "see more" link (though, do be careful — very few reviewers will be willing to click through and read thousands of lines of your code), but the most important parts of the code must be placed directly in the question.