From Copenhagen, the most convenient way to reach Fredensborg is to catch an S-train to Hillerød, and change to the Lille Nord (http://www.lokalbanen.dk/...) train towards Fredensborg and Elsinore Helsingør, which sees departures towards the city twice per hour most of the day. It is possible to use the same line from Elsinore. The trip from Copenhagen takes about an hour.
It is also possible to catch a bus from Humlebæk Louisiana Art Museum, bus 844 and 733E, 25 minutes. From Nørreport station in central Copenhagen there is a is a rushhour express bus 6AM-9AM, 1PM-5PM, which completes the journey in 45 minutes bus 173E
If you have your own wheels take the Helsingørmotorvejen highway E47 and E55 to exit 7 Kokkedal, turn left, and follow Fredensborg Kongevej to the end.