Here you need to describe the various features that you would like to have in your "Paternity Leave" like whether it should be an allowanced leave or a non-allowanced leave. And various other options like "Event Visibility, Restrictions,Cover" can be set here on this page.
After you have created the leave type you need to click on the "Submit" button at the bottom of the page and you will get a new leave type listed in your events and allowances page. See the below snapshot:
Then any user can request for a paternity leave by clicking on the "Request Leave" button on the home page. The "Paternity Leave" option would be listed in the "Type" drop down box for him.