Do I need anything installed locally to use GitHub other than what I already use for development?
Not necessarily. You can do it all through the GitHub web interface. However, using git on your local machine can make things easier: you can use your own choice of editor, save your work part way through, run local tests, etc.
Do I need to get permission/acceptance from the maintainer?
Not up front, no. When you make the pull request the owner of the repo will be alerted to it and will either accept it or respond with feedback prior to accepting. If you refer to the issue that has already been raised in the PR text that will help.
There is some general guidance here but essentially the process is
- Obtain a github account if you don't already have one.
- Fork the repo
- Make changes to your fork
- Raise the pull request