Our hosting service is Netlify.
The production branch is configured to be automatically deployed to
https://profiler.firefox.com.
In addition to this pushes to the main branch deploys to the domain
https://main--perf-html.netlify.app. Every pull request will be deployed as well to a
separate domain, whose link will be added automatically to the PR:

The easiest by far is to create a pull request on GitHub. It would be nice to write down the main changes in the PR description.
After the PR is created all checks should run. When it's ready the PR can be merged. Be careful to always use the create a merge commit functionality, not squash or rebase, to keep a better history.
Once it's done the new version should be deployed automatically. You can follow the process on Netlify's dashboard if you have access.
The easiest way is to reset the production branch to a previous version, and force push it. You'll need to enable force-pushing for the branch production, using the Branch Settings on GitHub.
You can use the following script:
sh bin/revert-last-deployment.sh
When you're ready with a fix landed on main, you can push a new version to the
production branch as described in the first part.