You need to copy the repo to your git-hub and work on it for that follow the steps:
Create a new repository in your github
Then clone the repository which you need to work on from your hosted.org to the local machine
Then rename the repo with upstream using:
git remote rename origin upstream
Then add your repository url to your remote using:
git remote add origin <url>
Then push the changes to your remote repo using:
git push origin master
From the above steps, you can copy repo to your github.
To get updated and to pull the changes you can do:
git pull upstream master && git push origin master
This will pull the changes and keep you updated with your official repo.
To learn more about Git version control system then you can enroll in Github Training.