Don't understand about the Schengen area visa system, for staying in Denmark specifically? [duplicate]

According to the text of the EU freedom of movement and residence law summary:

European Union citizens have the right to move freely and live in another EU country, subject to any conditions set out in the EU’s treaties. This free movement of people is one of the EU’s fundamental principles.

EU citizens with a valid identity card or passport may:

• Enter another EU country, as may their family members - whether EU citizens or not - without requiring an exit or entry visa.
• Live in another EU country for up to 3 months without any conditions or formalities.
• Live in another EU country for longer than 3 months subject to certain conditions, depending on their status in the host country. Those who are employed or self-employed do not need to meet any other conditions. Students and other people not working for payment, such as those in retirement, must have sufficient resources for themselves and their family, so as not to be a burden on the host country’s social assistance system, and comprehensive sickness insurance cover.
• Have to register with the relevant authorities if living in the country longer than 3 months. Their family members, if not EU nationals, require a residence card valid for 5 years.
• Be entitled to permanent residence if they have lived legally in another EU country for a continuous period of 5 years. This also applies to family members.
• Have the right to be treated on an equal footing with nationals of the host country. However, host authorities are not obliged to grant benefits to EU citizens not working for payment during the first 3 months of their stay.

So there are some conditions, such as registering with authorities if required (which is required for Denmark), but generally you have the right to live in Denmark as long as you can afford it.

Specifically for Denmark, see http://www.nyidanmark.dk/en-us/coming_to_dk/eu_and_nordic_citizens/eu-eea_citizens/residence_in_denmark_for_union_citizens_and_eea_nationals.htm. This is the official government-run immigration website, and its information is trustworthy.

You're supposed to apply for a registration certificate if you stay in Denmark for more than 3 months, and to register yourself with the civil register (folkeregister) before 6 months of stay.

The Aliens Act (Udlændingeloven) contains a general punishment provision for aliens who reside in Denmark unlawfully: a fine or imprisonment up to 6 months. This range is supposed to cover all cases of illegal immigration from any country; it would be extremely theoretical that a jail sentence could be imposed on an EU citizen who would have an automatic right to a registration certificate but merely neglected to apply for one due to laziness or unawareness of the rules. I have no idea how likely a fine is and how large it might be.

As a British citizen, you shouldn't worry much. Keep in mind that it would be perfectly legal for you to fly to Spain, take a train to France, bicycle to Germany, and take a car to Denmark. After the airport in Spain, there would be no record of your border crossings unless you happened to get into a random spot check.

That being said, Henning pointed out that some EU countries try to keep track of all residents. Registering some time soon is a good idea. Also, that might help your position if the UK decides to leave the EU.