The Danish national rail operator DSB operates regular train services between Copenhagen and towns across Denmark and southern Sweden. A train from Copenhagen to Aarhus will take three hours, to Aalborg four hours and to Odense an hour and a half. You can see train routes, find times and book train tickets with DSB by calling +45 70 13 14 15. There is also the option of booking via the DSB website, where they have a handy tutorial for how to use their Danish booking system.