At the moment you start with a (part-time) job you are obliged to take out a Dutch health insurance. This also applies to an internship for which you are paid at least as much as the Dutch minimum wage. In the flyers of the Zorgverzekeringslijn you will find all the information you need about how to take out a Dutch health insurance and when you are required to have a Dutch health insurance for study or work (internship) in the Netherlands. The Youth Information Point (JIP) is another useful website that explains health insurances in the Netherlands.
More general information is available on the website of the Zorgverzekerlingslijn. In case you need advice or tips how to solve health insurance issues you can contact the Zorgverzekeringslijn.