There are two types that are usually used - general anesthesia and local with IV sedation.  Local anesthesia alone may be used for a minor procedure on the nose, but not for rhinoplasty.  With general anesthesia, the patient is put completely to sleep with a tube passed through the throat which administers the anesthetic gases and keeps blood from the back of the nose from going into the lungs.  With local anesthesia and IV sedation, a drug is given through a vein in your arm or hand which causes you to lose consciousness and the nose is injected with a local anesthetic.  With the nose anesthetized, less drug through the vein is used to keep you semi-conscious but you have to be conscious enough to breath on your own so if blood enters the lungs, you will still have a cough reflex and be able to clear your airway.