If you've ever been out in severe temperatures, you'll appreciate that 'cold' hurts. For small skin lumps, cryosurgery is temporarily uncomfortable, but for larger lumps, sedation and local anesthetic is required in order to keep the patient still enough to freeze the lump. For more delicate cryosurgery, such as on oral tumors or anal furunculosis, then anesthesia is required.
The vet will assess each case for suitability for cryosurgery. Hair needs to be clipped from around the lesion, but surgical sterility is not necessary. The surgeon is most likely to use liquid nitrogen contained in a special device with a probe attached to the end. The probe is placed against the lesion and a trigger pulled, which super chills the tip of the probe and anything it is in contact with.
The tip is held in place until a freeze halo a few millimeters wide develops around the lump. Then the trigger is released and the surgeon waits for the tip to thaw to release it from the tissue.
This freeze-thaw cycle is repeated two to three times.