Research Danish classes in your area. If your area has a significant Danish or northern European population, there may be classes available at a local community center or through a private instructor. You also might find a class at a nearby university or college.
Explore Internet language resources. There several places online that will help you speak Danish for no cost. Speakdanish.dk is a Danish site for foreign students of Danish, complete with excellent resources and detailed grammar lessons.
Read, don't just speak. You will increase your speaking ability by practicing your reading. Like English, many Danish words are pronounced differently from how they are written. Read out loud to yourself to improve your comprehension and spelling.
Find a conversation partner, or start a conversation group. You can ask people in your language class to meet up for coffee and Danish conversation, or you can advertise on the Internet. If there are no other students of Danish in your area, try an online language-learning and conversation site such as Live Mocha.
Immerse yourself daily in Danish language and culture. Surf Danish sites on the internet, or look up online radio stations in Danish. Try to speak, read or write some Danish every day. If you can, travel to Denmark to hear the language all around you.