just go down the line of local dentists in the phone book (if your own is not available), visit their office and tell them that you are considering dentistry as a career and would like to get an idea of what it is like in the office and ask them politely if they wouldn't mind you watching them for a few hours a week (most schools have a minimum of 40-50 hours) Many dentists are willing to let people shadow them but only if they can tell that you are going to take full advantage of the opportunity and not just take up space (by that i mean intently watch what they are doing and respect them and the assistants).
as for proving it, usually you can ask them for a recommendation if the experience went well. Some dentists do it often and have a generic letter that they use.
Look up dentists around your area on google maps. Visit their website and get to know their practice before you visit. So during your first meet and greet with the dentist you can bring up the website and start a conversation and show him/her of your interest in shadowing.
Many schools require a recommendation letter from a dentist. Simply request to have the number of hours included in that letter.
