Adding a collaborator to my free GitHub account?

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

Screenshot:

Clear Instructions On How to Add A Collaborator - 2020 Update

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

Picture Instructions (Click to Zoom in):

.......and videos/gifs are worth another thousand more:

Gif Instructions (Click to Zoom in):

Hopefully the pictures/gif make it easier for you to configure this!

It is pretty easy to add a collaborator to a free plan.

1. Navigate to the repository on Github you wish to share with your collaborator.
2. Click on the "Settings" tab on the right side of the menu at the top of the screen.
3. On the new page, click the "Collaborators" menu item on the left side of the page.
4. Start typing the new collaborator's GitHub username into the text box.
5. Select the GitHub user from the list that appears below the text box.
6. Click the "Add" button.

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 The instructions above are outdated, in particular step 2: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