Find a Drupal 8 core issue you would like to work on.
Visit the Drupal Mentoring task tracking tool, and create an account if you don't have one already.
Add a new task for the core issue you found.
On the new task you created, click the "+ Add" link below the "Task Attempt" header, to indicate that you're going to work on the task. Put your user name in the Mentor field and click Save.
Jump in and see if you can reproduce the issue.
Post a comment to the issue with your results (for example, "I'm able to reproduce this issue; now checking xyz"). Also be sure to update the issue summary if you discover additional information.
During the issue sprint with your user group, meet up with the person who signed up as the Participant for your task. Pair up and work together on the issue.
Back in the issue tracker tool, leave comments indicating what you did. This can be pretty simple, such as: "left a comment on the issue with additional debugging information" or "reviewed a patch and left feedback."