First, your friend will need to add you as a collaborator on his repository. He can do this by going into the repository settings and inviting you as a collaborator by your username. Then you have to accept an email invitation. Then you will have push access to their repository from your account. Then you must fork their project repository to create a copy of it in your own account. Then clone this forked repository to your machine. Then you can push the changes to your forked repository. Then open up a pull request on Github from your fork to your friend's original repository.
Kindly, refer to docs for more details.