After being in private preview for few weeks/months, Visio Online is now available in public preview.
After getting GA later this year, Visio Online will require a paid license to create new Visio file; the viewing experience will be free.
This will be available on per user basis.
To start using Visio Online preview you need to ensure your SharePoint tenant is configured to enable preview feature (located within the Settings section of the SharePoint Administration portal) as shown below
Once enabled it may take some time to get it.
Once available, your user will be able to create Visio file directly from the SharePoint document library