Hello @Lukas16,
The guest should just tap or click on "Change or Cancel" and then "Cancel" when they are viewing their reservation with you.
That way they cancel the reservation. They will be refunded, by Aribnb, according to your cancellation policy.
They will loose whatever fee Airbnb charged them over and above your room charge.
Be very wary of cancellation requests. If you receive a communication saying that the guest has requested a cancellation always respond with "Decline". If you accept it you will be deemed to have cancelled and you will be penalised just the same as if you had initiated the cancellation. It's a very sneaky ploy by Airbnb. Your dates will be blocked, you may be fined and a "The host cancelled this reservation ..." review will be placed on your listing.
I'm a host. What penalties apply if I need to cancel a reservation?
For info on contacting Airbnb type "phone" in the "Search the community" box on the page where you see these questions and answers. You can also type "contact airbnb" there and pick the "Contact airbnb: A Community Help Guide" article that has the phone numbers, Twitter details and how to contact them via the website. There is no email address.
Steve.