You can get to Elsinore in North Sealand by ferry from Helsingborg in Sweden. But there are also local ferries in North Zealand. See alle the ferries here.
In North Sealand, you can easily get around by bus and train. Lokalbanen runs from Elsinore to Gilleleje and further to Hillerød, from Tisvildeleje to Hillerød, from Hundested Harbour to Hillerød and from Elsinore to Hillerød. It´s also possible to get around by bus.
If you want to fly to North Sealand, it happens via Copenhagen Airport, from which there are many both domestic and international routes. You can read about arrivals and departures, parking and transportation options and other amenities that make Copenhagen Airport your gateway to North Sealand on cph.dk.