Rhinoplasty is usually performed either with local anesthesia plus some sedation, or general anesthesia. Your surgeon may give you a choice here, but circumstance may preclude your choosing, or your surgeon may have a clear preference. As a rule of thumb, if your nose only needs a little reshaping, you can probably have local anesthesia. If you need more extensive work, you will probably need general anesthesia.
If you are having local anesthesia for your rhinoplasty surgery, you will receive sedative medications that will relax you and keep you calm. You quite possibly will fall asleep. The sedatives may be administered through an intravenous (IV) line into a vein in your arm or you may be given pills to take. Even if you stay awake or wake up a bit during the procedure, you will be so relaxed you will not care. When you are relaxed and sedated, your surgeon will inject local anesthetics, such as lidocaine. He or she may also inject a drug called epinephrine, which will constrict the blood vessels and help reduce bleeding. The injections feel pretty much like getting any injections; you will feel a sting for a few seconds and then the area will start to go numb. Usually, you will get several injections over the area of your mid-face.