Hi eharr,
Depending on what you have selected in Events > Settings > Template you’ll need to modify that template file.
If you have the “Default Events Template” selected, you’ll want to make a copy of /wp-content/plugins/the-events-calendar/views/ecp-single-template.php and place in an ‘events’ folder in your theme and then modify it to remove the title and other information.
If you have the “Default Page Template” (or other theme template) selected, you’ll want to open up your theme’s single.php and then modify it to remove the title and other information. If you have this template option selected you’ll need to conditionally modify things with some of the following conditional code: https://gist.github.com/jo-snips/2415009
I hope that helps but let me know if you have any questions.
– Jonah