Denmark issues a residence permit for higher education, applied for after you hold an offer from an approved institution. The process is well documented and comparatively predictable, and its failure mode is almost entirely sequencing rather than substance.
The order is offer, then case order identification and fee payment, then application submission, then biometrics at the mission. Doing any of these out of order produces a file that sits unprocessed while the applicant waits for a decision that has not begun.
Funds and fees
Applicants from outside the EU generally pay tuition, and evidence that the first instalment is paid or that a scholarship covers it is normally part of the file. You will also need to show you can support yourself for the study period.
Danish living costs are high. An application that satisfies the formal requirement but assumes an unrealistic monthly budget tends to produce a difficult first year even when the permit is granted.
Housing
Housing in Copenhagen and Aarhus is competitive and expensive, and institutional housing offices allocate limited stock. Start the search when the offer arrives, not when the permit does.
You will register your address after arrival to obtain a personal identification number, which most practical services depend on.
Working during study
Work rights attached to the study permit are real but limited, and they should be treated as a supplement to a funded plan rather than as the plan. Applications that rely on projected earnings to close a funding gap are weak applications.
Model the year on the money you actually hold. That is the standard the caseworker is applying too.