If you are just adding new emoji or making a small fix, only increment the patch level "1.0.x". If you need to rename a ton of emojis or making any other radical (but still mostly backwards compatible changes), bump the minor version "1.x.x".
To prepare the release commit, edit the gemoji.gemspec version value. Then make a single commit with the description as "Gemoji 1.x.x". Finally, tag the commit with v1.x.x.
Example commit https://github.com/github/gemoji/commit/v1.0.0
$ git ci -m "Gemoji 1.0.0"
$ git tag v1.0.0
$ git push
$ git push --tags
Build and push the new gem with
$ gem build gemoji.gemspec
$ gem push gemoji-1.0.0.gem