Navigate to your profile page by clicking your name in the top-right corner and clicking the "My Profile" link.
In the top box on the page - where your name and profile picture appear - you'll see a yellow "Edit" button on the right side. Click there to open the "Edit Profile Details" pop-up.
The second field will be for your headline. Add your headline there and click the yellow "Update" button at the bottom when you're finished.
For what the headline section is all about, see this article:
For more articles on getting started on ZMZ, see this collection!