+1 to ask your dentist.
You want to position yourself in the operatory so you can see in the patients mouth, while not being in the way of the dentist/assistant. I found that to be tricky'er than it sounds lol
The shadowing really depends on the personality of the dentist. The dentists I shadowed were all really cool and would talk through the procedures as they went.
You also want to be careful not to ramble off 1,000 questions while they are filling out charts or thinking through something, or in the middle of a complicated procedure.
I found that between patients/procedures is the best time to chat them up. Even if you don't have any questions, try to have SOMETHING to ask so it's not akward.
At the end of all my shadowing, the dentists always told me "your welcome back whenever" and that they always get some wierdos shadowing that they would never want back into their office. So if you are a normal person with a personality you should be fine.