The best way to work with Gnulib is to check it out of git.
To synchronize, you can use
Subscribing to the email@example.com mailing list will help you to plan when to update your local copy of Gnulib (which you use to maintain your software) from git. You can review the archives, subscribe, etc., via https://lists.gnu.org/mailman/listinfo/bug-gnulib.
Sometimes, using an updated version of Gnulib will require you to use newer versions of GNU Automake or Autoconf. You may find it helpful to join the autotools-announce mailing list to be advised of such changes.