Question

How do you contribute to repos that you do not have push access to on github?

Answer 1

You make a "pull request" (to ask them to merge changes from a repo that you do have access to, such as own personal fork on GitHub.)

Answer 2

Once changes are pushed back up to your forked remote repo, notify the maintainer of the parent repo that you have made some changes and issue a "git request" on GitHub. Then the maintainer reviews the pull request and merges them in if they liked the changes you made.