The Dutch word for dentist is 'tandarts'. Almost all dental practices in the Netherlands are private, there are no state practices.
Many of the Dutch practices are full an it can be difficult to find one able to take on new patients. A dentist can be found via the website tandarts.nl (in Dutch). Another option would be to contact your health insurance agency to request a list of practices that are accepting new patients.
In general, dental treatment is not covered by your health insurance. Dental care can only be insured by taking out an additional insurance.