I shadowed my life long general dentist, for a whole summer actually, a few times a week. That same dentist has other dental friends (oral surgeons and endo). Then I knew a friends mom who worked in a dental office, she got me in to shadow a few weeks there, with both dentists who work there. That same dentist's husband (friends mom's office) is a periodontist, and shadowing there got me in to shadow with him. Funny thing is that the periodontist decided to stop having people shadow because the past 2 people who shadowed had to leave mid-appointment (because of the nature of periodontal issues that people can have), but he was kind enough to ask my friends mom and his wife if I would be able to handle a whole day of periodontal procedures. It was a great experience.
Moral of the story, get in to shadow one dentist, if the days spent there go well, they will refer you to other offices if you ask.