We operate the "Fork & Pull" model explained at
https://help.github.com/articles/about-pull-requests/
You should fork the project into your own repo, create a topic branch there and then make one or more pull requests back to the osm-carto-tutorials repository. Your pull requests will then be reviewed and discussed.
You can use Git Desktop to clone the repository.
To save the credentials:
git config --global credential.helper cache
To set the vi editor:
git config --global core.editor "vi"