Issues that have been assigned to you will show up on your dashboard page. You will also receive a notification letting you know you have been assigned to an issue. Click on the issue in the dashboard list or the notification to open the issue. Scroll to the bottom of the issue drawer on to leave a return comment. The issue creator will receive a notification letting them know you've commented on the issue.
When a new comment has been made on an issue thread, the owner, assignee, and any other user who has commented, will receive a notification. The notification can be viewed by clicking on the bell icon in the bottom corner of the left sidebar.