try to make it as casual as you can but act like a professinal (if it makes any sense). since you will be mostly observing the dentist (and not the hygienist) try to befriend the dentist as he will serve as your mentor and mostly likely write you a LOR. Try meeting him in advance (in his office) or arrive early that day to just chat and try to make a good impression. he is doing you a favor afterall. always be thankful and try satying out of everyone's way. when i shadowed my dentist friend, he just went over the problem with me; explained what was wrong, pointing to the x-ray and said what he will do (most of this was also in the conversation form directed to the patient). often he elaborated on certain things too, especially when the patient was gone and he couldnt say those in front of the patinet or wanted to justify his rational for saying/doing something instead of something else. so a good relationship with the dentist can make a world of difference. If i were you, i'd ask the dentist to point out things that you might not fully appreciate while observing. I am sure he wont mind showing off some knowledge. You are there NOT to learn detistry but to get a feel of the profession as in what sort of stuff they have to deal with; managing a business, working in a team, dealing with uncompliant patinets, being a professional, and rendering treatment is only ONE of the things he will be doing. so try to look at the the bigger picture. i also talked a lot to the assistant while they were setting up/cleaning the rooms.. they tought me a lot about all the little tools and their uses. be inquisitive and you will be just fine.
best of luck to you.