Here are most of the steps we (maintainers) follow when making a release.

* start from a clean, up-to-date git directory.

    git checkout master; git pull

* Run ./configure && make maintainer-clean

* Ensure that the desired versions of autoconf, automake, etc.
  are in your PATH.  See the buildreq list in bootstrap.conf for
  the complete list.

* Ensure that you're on "master" with no uncommitted diffs.
  This should produce no output: git checkout master; git diff

* Run bootstrap: ./bootstrap

* Pre-release testing:
  Ensure that make check syntax-check succeeds.

* Run "make distcheck"

* Set the date, version number, and release type [stable/alpha/beta] on
  line 3 of NEWS, commit that, and tag the release by running e.g.,

    build-aux/do-release-commit-and-tag 8.1 beta

* Run the following to create release tarballs.  Your choice selects the
  corresponding upload-to destination in the emitted gnupload command.
  The different destinations are specified in cfg.mk.  See the definitions
  of gnu_ftp_host-{alpha,beta,stable}.

    # "TYPE" must be stable, beta or alpha
    make TYPE

* Test the tarball.  copy it to a few odd-ball systems and ensure that
  it builds and passes all tests.

* While that's happening, write the release announcement that you will
  soon post.

Once all the builds and tests have passed,

* Run the gnupload command that was suggested by your "make stable" run above.

* Wait a few minutes (maybe up to 30?) and then use the release URLs to
  download all tarball/signature pairs and use gpg --verify to ensure
  that they're all valid.

* Push the NEWS-updating changes and the new tag:

    v=$(cat .prev-version)
    git push origin master tag v$v

* Send the gpg-signed announcement mail, e.g.,

    To: info-gnu@gnu.org
    Cc: coordinator@translationproject.org, bug-gzip@gnu.org
    Subject: gzip-1.3.13 released [stable]

* Announce it on Savannah, too:
  From here:
    https://savannah.gnu.org/projects/gzip/
  click on the "submit news", then write something like the following:
  (If there is no such button, then enable "News" for the project via
   the Main -> "Select Features" menu item, or via this link:
   https://savannah.gnu.org/project/admin/editgroupfeatures.php?group=gzip)

    Subject: gzip-1.3.13 released [stable]
    The announcement is here:
      http://article.gmane.org/gmane.comp.gnu.gzip.bugs/258

  Then go here to approve it:
    https://savannah.gnu.org/news/approve.php?group=gzip

* After each non-alpha release, update the on-line manual accessible via

    http://www.gnu.org/software/gzip/manual/

  by running this:

    build-aux/gnu-web-doc-update
