When you have a calendar connected in your Doodle account, a calendar invitation will be sent out automatically once you select the final option - you don't have to take any further action.
Even if you invite your participants via link sharing, and not by email, the participants are required to enter an email address before voting. The calendar invitation will be sent to the email they provided when they voted.
The calendar invitation will be sent to all participants - even the ones that did not select the option that was picked as the final option. Their invitation will automatically be declined, thus making sure that the event does not take up a slot in their calendars.