By train
The vast majority of regional transportation is done by train, the bulk of it on the 4 main DSB (http://www.dsb.dk) corridors, radiating out of Copenhagen. It is worth noting that that the ticketing system changes in Borup and Hvalsø, roughly half way between Roskilde and Holbæk & Ringsted respectively, if you cross these cities "All-Zone" tickets bought in Copenhagen are no longer valid, and you need to purchase train tickets with DSB instead,
North
Copenhagen-ElsinoreWest
Copenhagen-Holbæk-KalundborgSouth-West
Copenhagen-Ringsted-KorsørSouth
Copenhagen-Ringsted-Nykøbing FalsterBy bus
The regional transportation agency for the whole region is Movia (http://www.movia.dk). Though the lionsshare of long distance transportation in the region are done by train, there are a few important interregional routes namely:
60
Vordingborg - Maribo Lolland62
Vordingborg - Stege Møn64
Vordingborg - Bogø - Stege MønAnd two mainly summer express buses (http://www.hurtigbussen.dk) which non-stop between Høje Taastrup and the beaches and vacation homes in North-Eastern Zealand:
555
Høje Taastrup - Holbæk - Odden ferry to Jutland666
Høje Taastrup - Nykøbing Sjælland - Rørvig ferry to HundestedBy ship
The most important ferry route on Zealand is between Hundested and Rørvig (http://www.hundested-roer...), crossing the big fjord in northern part of the island. Many of the smaller islands dotting the sea around Zealand and Lolland are also connected by ferries, check these in the relevant sub regions,