Submerge yourself in the language ;) If you don't have a class available to take, you might want to try an app such as Duolingo. It's not something you learn overnight, but it should help you get started!
Duolingo, I guess. I'm not sure if it's the best way, but it's free, and for courses that have been out of beta for a while (as I think Danish is, although I haven't done it myself yet) it's generally quite good.
Reading on the side is probably also quite important, for learning more ways of saying things, and more vocabulary.
Hm, I'm not sure. I personally find it difficult to understand lyrics in most pop songs, especially if they are in English. Poetry also generally strays more from the conventions of a language than prose.
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