Learning just basic Danish is a expected to some degree from exchange students, even most Danes are very good at speaking English. Of course we won't expect much from short term students.
Most high schools (gymnasie) offers free Danish course for their exchange students. If they haven't given information about this, contact the school administration and ask or have your host family reach out to the school. Some schools cooperate on this.
Below we'll list a number of public Danish courses you can sign up for. Be aware there's a mandatory deposit at dkr. 2.000,- which will be returned when you have passed the course.
Kastetvej 26, 9000 Aalborg.
Tel. 99 31 58 10
Website (Unfortunately, their website is in Danish only)
Offers free Danish courses. It is possible to attend either online or physical location courses.
No information on physical location Danish courses at Læsø. We refer to online courses.
Refering to Aalborg Sprogskole. See Aalborg Kommune for further information.