DSB (Danske Statsbaner), the Danish State Railways, cover together with the private train company Arriva and few other train companies the entire Denmark with train services. Those are supplemented by buses on quieter stretches.
The modern Denmark InterCity train connects Copenhagen and Zealand every hour.
A train for Odense on the island Funen goes every half an hour and the journey takes only 1 hour and 25 minutes.
Aarhus can be reached by train from Copenhagen within 3 hours. This service is provided by InterCityLyn, which is a fast train with few stops.
There are two categories in the InterCity trains:
Business – former 1st-class
Standard – former 2nd –class
If you are planning to stay in Denmark for longer than two days and would like to travel around the country by train it is worth to purchase InterRail Denmark Pass. Its validity is from 3 to 8 days (different prices vary from class, special discounts and validity) and you are also entitled to various extra pass benefits in Denmark such as discounts or free shipping services, validity on the private railways or a discount to the railway museum in Odense.