When your website is built in a way that tells the search engines exactly what it is about. Your website pages have to be built around the services you are providing and contain all the related search queries which your future customer might use to find your service or dental practice. This will account for ON-PAGE search engine optimization.
Additionally what is necessary is to submit your accurate business information to all the major relevant directories. Publish press releases and articles which your local audience will read and link back to your website. Linking back to your website can be done also from other relevant websites. This is what you can consider as OFF-PAGE optimization. Which is much more intricate process that can be covered at this time.
All of these elements combined will tell all the major search engines like Google/Bing/Yahoo that your website is relevant to what your future customers are searching for. And will also show that other websites are linking back to your web property. Which in summary will increase your rankings in all of the major search engines.
Since first result usually gets one third of all the visitors. You now understand how important it is to build up and promote your asset.
If your website will get more visitors who are interested in your services, it will equate with increased number of new patients.