Everything happens in the item’s “Booking” tab, “Upcoming sessions” table.
Cancelling a session
Click “Cancel”: the session no longer accepts new bookings and shows as “cancelled”. Orders already placed remain: one click on the session shows the orders and the number of places, so you can let your participants know. Then refund their orders, or offer them another date. Changed your mind? “Reopen” puts the session back on sale.
Moving a session
There is no “move” button: a booked date commits your customers, so it is up to you to tell them. Add the new session, cancel the old one, then contact the participants to offer the new date or a refund.
Deleting a session
A session with no bookings at all, created by mistake for example, can be deleted. A session that has bookings can only be cancelled: that way you keep track of every participant.
See also: How do I offer bookings for classes, workshops or events?, Where can I see all my bookings for the week?