From Copenhagen Airport:

Car rental please use the following link Car Rental - Copenhagen Airports

Take motorway E47/E55 towards Helsingør (Elsinore). The motorway stops just outside Elsinore and becomes the E47/E55 Kongevejen. Turn left into Klostermosevej at the second roundabout. At the end of Klostermosevej turn right into Esrumvej. Continue to traffic lights and turn left into Gefionsvej. At the end of Gefionsvej turn left again into Gl. Hellebækvej after approximately 500 meters turn right.

See this zoomable map for details Roadmap of Elsinore (6)
 

From Malmö Airport:

Car rental please use the following link Car Rentals- Luftfartsverket.

Take the E65 towards Köpenhamn (Copenhagen). Cross the Øresund Bridge and follow the instructions above.

You have to pay to cross the Øresund Bridge for further information please use the following link ØresundsBron