Most Danes speak English quite well. Nevertheless, being able to speak some Danish will benefit you both socially and if you want to look for a job.
Language Courses for free
The majority of universities in Denmark have Danish language courses for international students either pre-semester or in the beginning of the semester. Check with your local international office when you arrive if it’s not mentioned in your admittance package.
If you would like to continue studying Danish, there are numerous private and public centres offering free language courses for internationals. You just need to have a CPR number to sign up. (So that is one more reason to get it done in a hurry…)