A link was graciously provided to a PR on GitHub to fix an issue that I am watching in the Jira issue queue. The fix is only one line of code that changes a display, so I am confident applying the fix without upgrading my installation will not have unintended consequences in this particular case.
Obviously, I can change the one line of code by hand, but in the interest of trying to use best practices, I'd like to understand the best way of using Git itself to apply the change. I have Git installed on my server and use a private GitHub repository for our organization's code base.
The "GitHub for CiviCRM" documentation (http://wiki.civicrm.org/confluence/display/CRMDOC/GitHub+for+CiviCRM) is geared towards those contributing to the codebase rather than those who need to apply a supplied fix.