This is the poor person's version of hosting a chart on GitHub, most examples show how to use GitHub Actions with GitHub Pages, but that's not necessary for the short term.
The Helm chart only requires that the file index.yaml be accessible from the Helm URL that is provided. The index.yaml can then point anywhere you like to host the bundled tar file with the chart.
Therefore, this example just relies on giving a GitHub raw link to the index.yaml and we put the tar file in the same location. We could easily publish a GitHub version and use the version url for the tar file but that requires more steps. See https://github.com/helm/chart-releaser It looks easier to use but you need to generate a token. Would be nice if it used your ssh credentials from the local repository or something.
Create a branch, edit the template, values, Chart, whatever. Commit the changes and push.
This is important: make sure you edit Chart.yaml and update the semver. It is possible to use helm commands to update the version too.
This will create a tar file with the contents of the directory, like releaes-ingres-0.0.0.tgz. It will include the previous tar version too :P This is the world's lamest version of tar cvfz . written in Go for people who don't know Un*x.
helm package .The repo index will be overwritten by default, so we use --merge. The URL is the GitHub raw link to the repository root where the index.yaml will be.
helm repo index . --merge index.yaml --url https://raw.githubusercontent.com/releasehub-com/helm-ingress/main/Check git diff to see changes to index.yaml. Deprecate previous versions as necessary.
Push your changes to the branch, ask for a code review and then merge.