The easiest entry points are Hillerød and Elsinore. Hillerød is reached with the E line of the S-train system 44 mins, from there you can catch a small local railway which runs to either Gilleje or Tisvildeleje/Helsinge once or twice an hour throughout most of the day. Hillerød is also the main terminal for bus routes in the area. Another option is Elsinore at the end of the kystbanen railway from central Copenhagen 45 mins from there you can another small local railway to Gilleje running along the coast. The whole trip from Copenhagen Central station to Gilleleje takes around 1,15 hours via Hillerød and and 1,45 hours via Elsinore.
There are plenty of options for driving and routes naturally depends where exactly you are going, but generally you take the Hillerødmotorvejen route 16 motorway towards Hillerød for destinations west of Gilleleje, while the Helsingørmotorvejen route E47/55 motorway towards Elsinore is fastest for destinations to the east.
