When in Copenhagen the cheapest and often fastest way to get around the city is using public transportation. And the cheapest way is with a Travlecard (Rejsekort) these cards can be purchased in small stands like the one in the image below, or in most 7/11 shops. These stands can be found on almost all major train stations. (and in the airport) When traveling from the airport to the central Copenhagen there is both the intercity trains and Metro going to the Central part of Copenhagen.
Using a “Rejsekort”
When using a Rejsekort it is expected of you to check in on the stands that are on every station, or in every bus. the stand has a large blue circle with the words “ind” every time you enter a form of transportation. (This can be as said, train, bus, ferry and so on) only when you are finished with your complete trip will you need to check out, this works the same way as checking in, just touch it on the stand that says “ud” instead. You can ride multiple people on one “Rejsekort” but you will need to find a stand that has a some additional features, it will say “Extra” on the top of the stand, and there will be some buttons that you can press.
How it works:
Other transportation methods include, Bikeing, (You can rent bikes loads of places) electric scooters, (They have started to allow electric scooters to be used in Copenhagen, PLEASE WEAR A HELMET!) and Taxis. (Taking a cap is really expensive, and have a start service fee of around 50 DKK depending on the time of day) Services like UBER has been banned in Denmark, although some drivers are still around.
Knowing your way around
In Denmark DSB has provided a service called Rejseplanen, (Travleplan) its a mobile and web app that you can use to figure out what public transportation you will need to get around Denmark. Google maps can also be used, but is not as updated as rejseplanen in regards to delays. Rejseplanen can be downloaded as apps on both Iphoens, Androids and can be found online on https://rejseplanen.dk
Staying in Copenhagen
Hotels can be quite expensive, if you are traveling alone, or feeling adventurous then the Hostels are in the same price range as others in Europe. Renting AIRBNB will in most cases be as expensive as hotels. If you take a train about 10-15 minutes out of the center of Copenhagen then the prices for hotels drops off a bit.