How do I file for an health care exemption? The healthcare.gov website says no applications are necessary with 2018 tax period.
This is true for hardship exemptions:
Starting with plan year 2018 (for which you’ll file taxes in April 2019), you don’t have to fill out an application to get a hardship exemption. You can claim the exemption, without having to submit documentation about the hardship, on your 2018 federal tax return.
For the other exemptions go to this site and "Find Exemptions":