I started with my family dentist. At my appointment, when he came in the for the exam, I asked him. He was thrilled and wanted me to come in. After I was done with him, his office staff recommended a dentist in a neighboring town - and he too was excited to have me come in.
I would also recommend you to ask your friends and family to put out feelers for you. I find that technique to work wonders sometimes. If someone you know well tells their dentist, "Dr. X, I have a 'insert relationship here' that is looking to go to dental school and needs some shadowing experience first. You seem like a great person to learn from. Can I recommend to them that they contact you?" In my experience, often times the dentist will be more receptive, since you've been recommended by someone he/she already knows.