When adding or editing an event, you'll see a section titled 'Who can see this plan,' where you can choose between 'Friends', 'Close Friends', and 'No one'. When viewing an event, you can also access this setting at the bottom of the page — just look for 'Share with...'. 

When you share a plan with a friend, they can see the time, title, and photo. They can also see whether any of their other friends are in the plan, if they've shared it with them. 

Only the people in a plan can see the location, details, chat, and who else is going. 

When a plan is not shared with a friend, they can only see, on the calendar, that you're marked as busy. If you want the event to be completely invisible, simply mark yourself as 'free.'