It is quite easy to hitchhike in Denmark. People who pick up hitchhikers usually speak English. Destination boards are recommended. It is illegal to hitchhike on the highways, so it is better to use highway-entrances and gas stations. When crossing by ferry, try to get into a car that already paid for the ticket.
If you hitchhike from the southern part of Denmark (direction from Hamburg or Kiel, Germany), and continue in direction to Copenhagen, make sure the driver doesn't stop in Kolding. If he does, ask him to stop at the last gas station before Kolding. On the Kolding highway crossing there is no place to hitchhike and it is one of the worst places in Europe for hitchhikers.
Check out the Tips for hitchhiking article here on wikitravel if you are new to hitchhiking