The Danish State Railways DSB (http://www.dsb.dk) runs trains two train per hour Copenhagen 1-1½ hours and Nykøbing Falster 30 mins throughout most of the day.
If you are heading Towards Møn and the cliffs, You can connect to Movia (http://movia.dk)] line 62 towards Stege, the main city - where you can change to bus 632 to reach the cliffs, this connection is possible every 2 hours during daytime.
