as student it is free of cost to become member of an "A-kasse" (Unemployment fund).
You can be member with no cost for you as long as you are student.
And if you (we do not hope..) do not get a job after finish your education you can receive
"dagpenge"/money from the danish state. But only if you have been member at least
one year before ending study.
You do not mention the exact study you follow, but if it is an higher education, I will
recommend you to be member of "MA A-kasse". Go to the formular on MA A-kasses website here: http://a-kasser.dk/ekstern/ma-akasse-medlem.php
Another choice could be
"CA A-kasse" - http://a-kasser.dk/ekstern/ca-akasse-medlem.php
Both of these are for students and people with some higher education.
You just have to follow the above link and fill out the formular.
Please notice that the fomular can be more than one page. Click "næste"/next to go to next part.
After that you will receive email-confirmation from the A-kasse.