How can I help Yii by fixing bugs, from my local home PC?

My basic question is how can I setup my various git repositories (local-home-pc and github) so that I can work on my own projects and also help the Yii project by "pushing" bugfixes to yii core, documentation and submodules etc.

In the past few months I’ve learned quite a bit about how to use git. I’m working on my linux-pc with several development projects and would like to organize things so that I can work on projects and Yii at the same time. I also have a github account.

I’ve downloaded the latest Yii2 code and generated a project using the advanced template. I’ve been working on my own project and have discovered a bug in the gii submodule. I’m not sure about how I can submit my suggested bug fix.

One scenario would be to clone the yii repositories in my GitHub account, and then clone this account to my local pc. In the event of a bugfix I could push my changes to my Github account and then issue a pull request.

I think I could already manage this but it seems like the GitHub stage is unnecessary. Is it not possible that I can issue something like a "pull request" from my local pc to the main Yii repository in question? How do you developers out there mange this situation?