Upvote:13
The train station is located in terminal 3. From terminal 1 you can take a free shuttle bus to terminal 3.
There is a direct train to Odense every hour. Otherwise you can take one of the frequent trains to Copenhagen central station and change there for a train bound to Odense. The journey lasts a bit less than two hours.
Tickets can be bought at the ticket machines in terminal 3 just above the railway station. There is also a DSB ticket sales counter, located in terminal 3.
It's all straightforward. Just follow the signs.
For train schedules check http://www.dsb.dk