Where the control is
Open My bookings. Each booking that has not flown yet carries a cancel button, and pressing it asks you to confirm before anything happens. A booking that has already flown, or that you cancelled earlier, does not offer one.
What cancelling does
It marks the booking cancelled. That is the whole of it: the booking stays on the list with a cancelled stamp on it, moves to the cancelled tab, and stops counting down to departure.
No money moves, because none moved when you booked — see Paying for a booking. Nothing is sent to the airline either. This site takes bookings and keeps them; it does not hold a seat anywhere, so there is nothing to give back and nobody to tell.
It has to be the same session
A booking belongs to the browsing session it was made in, and so does the right to cancel it. Close the browser and that session ends: the booking still exists, but the list is empty and the cancel button is not there to press.
There are no accounts here, so there is no way to prove a booking is yours once the session has gone. If you need to be able to cancel, do it before you close the browser.
Cancelling twice
The second attempt says the booking was not found or is already cancelled. Both halves of that are worth reading: it is the same answer you would get for a booking that was never yours, because from the outside those two look identical.