Lærdansk and NetDansk
In terms of learning the language, the main route we have seen (and experienced) here is through Lærdansk (http://www.laerdansk.dk/en). People can register for Lærdansk after they have their CPR number. There is another group, possibly associated, called Netdansk (http://www.netdansk.eu/en/). With them, you can study online, for example, if you can't make it to a Lærdansk centre. With these groups you can get many hours a week of professional tuition, completely for free. (Well, if you ignore the fact that taxes are paying for it, of course.) I am not sure of the exact rules at the moment, but I believe it's something along the lines of up to 15 hours a week tuition for up to 3 years. Through Lærdansk you can also take the language exams you need to if you wish to apply for permanent residence.It is an amazing system, and I feel very privileged to have such a facility available to help people like me. It's made a great difference to the speed of integration possible for my partner and me, and for others we know who have recently moved to Denmark.
(I hope I have not broken rules by including these websites. I don't know if they count as commercial in terms of what you meant in your submission guidelines.)
Thanks for the submission. Actually my wife does the lærdansk program right now, since she can not attend classes due to her work schedule. It is fine, but for those who are not registered in Denmark, yet we advise they take a beginner course like transparant which helps them learn some useful phrases and knowing a bit of the language is a great benefit.
Yes, get registered as soon as possible, contact your kommune and get started learning Danish as soon as possible. It is free for the 1st 3 years.
No violations on the websites. They are fine.