For travelling longer distances. Easiest via Copenhagen Airport (CPH). There are direct trains to Odense from the airport train station (once an hour usually) or frequent trains to Copenhagen Central station (København H), where there will be trains to Odense (usually every 30 minutes). Note Odense may not be the final destination so display boards at stations may give names of towns in Jutland (such as Aarhus, Aalborg, Esbjerg). All intercity trains going west will stop in Odense. Travel time from the airport to Odense is approximately 2 hours.
Train tickets cannot be bought on the train. These must be purchased at the airport at the red ticketing machines (credit card). Price approx. 300 DKK (approx. 40 EUR) for a standard single ticket with full flexibility. Discounted tickets (so-called orange tickets) can be purchased online on DSB Train, but these need to be booked early, are binding to specific train departures and are non-refundable if you miss the train due to flight delays. Standard tickets can also be bought online.
For medium long journeys, we recommend the train via Hamburg, Flensburg and Kolding to Odense. Inexpensive saver fare Denmark tickets are available at Deutsche Bahn. Direct trains from Hamburg to Odense 3 times a day, travel time is 3:30 h. Other convenient connections from Hamburg every 2 hours, change in Kolding or possibly in Flensburg. Passport control when entering Denmark by the Danish border police.