Parking in a new city can be daunting as no one wants to get a costly fine or have their car booted or toured. Some new apartment complexes have parking provided but this is not common place and you may need to pay an annual fee for this. There are a number of public parking houses where you can take an annual subscription but there are usually enormous waiting lists for these places.You can buy monthly or yearly passes for the zones in the city or pay as you go using an app or one of the machines in the street. This link from Copenhagen Kommune gives you all the information you need and they also have a section about parking in Frederiksberg, where the rules are slightly different. There are a various apps you can use to pay for parking (mentioned in the link above) and you can add more time to your parking without having to return to your car in many cases.
If you are looking to get a residents’ parking licence (you need your CPR for this even if you are buying one for a .guest) this is the link for Copenhagen ,the one for Frederikberg and the one for Gentofte.
You will need a parking clock in your car (these are easily and cheaply available from petrol (gas) stations but you can, of course, get fancy ones too. When you are in a time restricted area you set the clock to the arrival time.
There are some parking rules you need to follow which may not be obvious, if you don’t want a parking ticket in Copenhagen.
Finally if you need a disabled parking licence search for Handicapparkering on your Kommune’s website.