Read release notes (be sure to click the release version heading to see the full notes).

Check out the (brief) generic release notes on joinmastodon.org

Make sure you have a copy of https://gitlab.com/sunbeam.city/mastodon/ cloned locally.

export NEW_VERSION=4.2.0  # change to actual new version
git checkout trunk
git fetch upstream --tags
git checkout -b merged-$NEW_VERSION
git merge v$NEW_VERSION
git checkout trunk
git merge merged-$NEW_VERSION
git push

Then check the "Jobs" page on Gitlab, and you should see the Docker image build happily running 🏃 It takes about 8 minutes.