Go to Manage Access page under settings (https://github.com/user/repo/settings/access) and add the collaborators as needed.
Screenshot:

Pictures are worth a thousand words. Let's put that to the test:

.......and videos/gifs are worth another thousand more:
Hopefully the pictures/gif make it easier for you to configure this!

It is pretty easy to add a collaborator to a free plan.
The added user should now be able to push to your repository on GitHub.
In the repository, click Admin, then go to the Collaborators tab.
FYI for future readers. The instructions above are outdated, in particular step 2:
2. Click on Settings button
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