Are you going in the OR or to his clinic? If it's the former, don't ask a lot of questions. Just watch; a lot of what you want to know may be answered if you're patient and pay attention. Otherwise, make a mental note of what you want to know and ask him a couple of questions afterward. If you feel like you need to ask a question during the surgery, ask his permission first. Some surgeons may get annoyed if you interrupt them when they're trying to concentrate on what they're doing. If you're going to be in clinic, fire away. Ask about what you see in the patient rooms, what he likes or dislikes about his specialty, whatever else is on your mind. Talk about your observations of how he interacts with patients. Ask if you can do a simple part of the history (ex. find out what meds the patient takes, or what previous surgeries they've had).
If you're going to be shadowing this same doc a second time, here's how you can really impress him as being interested: at the end of the session, write down something interesting that you encountered during clinic or in the OR (ex. a pt with arthritis). Then read up on it (ex. what are pros and cons of getting your knees replaced if you have arthritis), and discuss what you read with him the next time you go in there. It has impressed several docs when I have been doing this as a third year med student. If you do it as a premed on whatever level of understanding you have (even if you read a website geared toward laypeople like medicinenet), you will definitely seem interested and enthusiastic. Plus, if you read up a little on the subject, you will be able to learn something about the field, have more understanding about what is going on, and ask more intelligent questions the next time. 🙂