The correct way to report Emacs bugs is to use the command M-x report-emacs-bug. It sets up a mail buffer with the essential information and the correct e-mail address, firstname.lastname@example.org. Anything sent there also appears in the newsgroup news:gnu.emacs.bug, but please use e-mail instead of news to submit the bug report. This ensures a reliable return address so you can be contacted for further details.
Be sure to read the “Bugs” section of the Emacs manual before reporting a bug! The manual describes in detail how to submit a useful bug report (see Reporting Bugs). (See Emacs manual, if you don't know how to read the manual.)
Sending bug reports to the help-gnu-emacs mailing list (which has the effect of posting on news:gnu.emacs.help) is undesirable because it takes the time of an unnecessarily large group of people, most of whom are just users and have no idea how to fix these problem. The bug-gnu-emacs list reaches a much smaller group of people who are more likely to know what to do and have expressed a wish to receive more messages about Emacs than the others.
RMS says it is sometimes fine to post to news:gnu.emacs.help:
If you have reported a bug and you don't hear about a possible fix, then after a suitable delay (such as a week) it is okay to post on
gnu.emacs.helpasking if anyone can help you.
If you are unsure whether you have found a bug, consider the following non-exhaustive list, courtesy of RMS:
If Emacs crashes, that is a bug. If Emacs gets compilation errors while building, that is a bug. If Emacs crashes while building, that is a bug. If Lisp code does not do what the documentation says it does, that is a bug.