What is the best way to share code through GitHub for the purposes of this Q&A forum?
The best approach is if the project contains everything needed to run the code and produce the same results you are experiencing. This includes seeding database tables.
Do I simply include a link to the GitHub repository in the body of the question, or are there other ways?
A link is the most efficient way to direct a forum member to your source code on GitHub. From there the forum member can clone or zip the project files. In the case of cloning the repo, the forum member can update the source code and commit the changes with a note of what was changed. Plus the repo will show exactly what code was changed.