With all marketing you have to identify your target audience and what the competition are offering.
Then you have to set a budget and arrange for feedback on how much response any advertising campaign generates.
When a new associate start at our practice, we initially targeted any patients who had not been for over two years. We whittled out the bad payers, the obnoxious and then sent invitations out to the rest to rejoin the practice. We basically sent a welcome pack outlining what the practice was doing at the moment.
Another thing you could do is "introduce a friend". Basically get some business cards printed which you hand to existing patients when they leave the practice. On one side is usual business card information on reverse the patients name and a promise that if a new patient brings the card to their first visit to the practice that the patient who recommends them gets a £5 M+S voucher.
I personally always think when I see an advert for a dental surgery in the local newspaper what is wrong with the practice so would only do this as a last resort. If you need to advertise do it as an article rather than an advert
Hope this helps