Simply create an event. Click 'Make your event live'. If your event is public it will then appear in the Explore page. If it is private it won't.
Please note that your tickets will not be 'live' and available for people to book - either through the Explore page or through the web link inserted in your email invitation - until you have published them. To publish your tickets, go to "My hosted events", click on your event and click edit. Click on the ticket you wish to make live and click "Make live".
You do not have to invite people until you are ready.
When you wish to invite people simply go to your event dashboard in "My hosted events" and click on the Invite button.