Learning Danish is highly recommended when you settle here permanently, it is even mandatory for non european citizens who want residency permits. So as a foreigner, you usually discover pretty quickly after your arrival the joys of a Dansk Sprogskole (danish language school). The largest municipalities have their own language school for adults, more or less rich and equiped depending on the municipality budget.
The Nordsjælland school where I have done my study is apparently in the "rich" category. Education 100% free (well I wasn't asked to pay anything yet), e-learning classes, small groups courses on evenings or on Saturdays, teacher available by mail to correct your exercises in between classes, language lab in a computer room, books provided, CD-ROMs, dictionaries ... is luxury!
Add to this that they give you notebooks the first day of school, and that you can request the loan of laptops and printers to take home, I finally understood why we pay so many taxes!