Danish citizenship can either be obtained through birth-right - if at least one of the child’s parents is a Danish citizen - or a person can apply to obtain Danish citizenship (naturalization). The person must have been a permanent resident before she/he can apply for citizenship. Refugees are required to have had 8 years of legal residency in Denmark before they can apply for citizenship, and other migrants are required to have had 9 years of legal residency. There are special rules if the person applying is married to a Danish citizen or is stateless.
Application can be filled out online, or downloaded, printed and sent to the Ministry of Integration. There is a fee of 1,200 DKR for applying, and the procedure takes at least a year. The ministry handles the cases, but the parliament’s (Folketinget) citizenship committee determines the applications through a bill introduced every six months.
In Denmark, the requirements for obtaining citizenship are very strict, and were tightened in 2015. The demands concern Danish language skills, self-support, crime, public debts, declaration of allegiance and loyalty, and the citizenship test about Danish history and culture. However, it was recently decided that dual citizenship is allowed.
It is possible to apply for an exemption from certain requirements if the applicant is not able to meet the requirements because of illness or disability. Yet, there are still examples of people being rejected citizenship without any form of justification and in May 2015, the UN Human Rights Committee ruled that Denmark broke the UN Convention of the Rights of Persons with Disabilities in such a case.
The conditions are about:
• Signing a declaration of loyalty.
• Permanent residence permit and habitation in Denmark.
• Duration of stay (8 years for refugees, 9 years for foreigners).
• Criminal sentences (quarantine period or exclusion, depending on the length of sentence).
• Due debt to the state (you're not allowed to owe money to state or municipality).
• Self support (it is not allowed to have received kontanthjælp/integrationsydelse for more than 6 months during the last 5 years).
• Danish language skills (passed test of Dansk 3 or similar).
• Citizenship test 2015.
Read more about the specific demands on the website of the ministry (there are exceptions and details not mentioned above). Only a limited version is available in English.