Log on to your online bank and cancel the transaction in your account. If it is already pending, you might not be able to stop the transaction online. If the funds have been withdrawn already, you'll have to go through the bank or the vendor to reverse the charge.
Contact your bank. Some venues, such as Google checkout, don't get involved in canceling debit transactions, but a bank often will contact the vendor on your behalf.
Contact the vendor directly. Some vendors have policies that give buyers a few days to cancel orders. Even without a cancellation policy, they might be willing to work with you.
Cancel the debit card and order a new one from your bank. Although this won't solve the problem for purchases that are pending, it will cut off funding from recurring monthly payments tied to your debit card.