Start at the place you study
The place you study will often have good advice on how to find a cheap accommodation close to your study. Start by examining their recommendations.
Halls of residence
Many students prefer to live in halls of residence. This is both because it is cheap but also to get to know other students by living with them.
You can read more about the different halls of residence here, and you can get signed up on an urgent waiting list if you urgently need a place to stay.
At Study in Denmark you can find a guide to the whole application process. Here you can also find links to relevant housing portals and find more advice on search for housing as a student.