From the airport

Arriving in Copenhagen airport, follow the signs to the trains or to the Metro. Trains for Copenhagen city centre leaves from track 2 (under ground); they all stop at Copenhagen Central Station and most continue to Nørreport. The Metro line (1st floor) starts at the airport and makes stops at Kongens Nytorv and Nørreport stations, among others. Please note – tickets must be purchased before entering the train. You can do this while awaiting your checked-in luggage, as there are ticket vending machines in the baggage claims area. Between the city centre and the airport the ticket price is DKK 36 (€4.83).
Getting around in Copenhagen
The obvious way to move around in Copenhagen is on bike; for an hourly fee you can use the white City Bikes. Or you can get a less clunky version from one of the many city rental shops. Either way, make sure to observe the traffic rules for cyclists; you’re not alone out there!
There is also public transportation, of course. It is reliable and effective, and the system consists of busses, metro, ferries, and s-train. Tickets can be bought on busses (cash only) or in the vending machines (coins/credit card only) at the metro or s-train stations.

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The price is DKK 24 (€3,22) per trip for 2 zones. Please note that going between the city centre and the airport, you pass through 3 zones, bringing the ticket price to DKK 36 (€4.83).
You can buy unlimited city area passes for 24 or 72 hours (DKK 80/€ 10,73 or DKK 200/€ 26,82, respectively), or for a week (from DKK 250/€ 33,52, depending on number of zones)
You can find more information on the ticket system here: http://www.dinoffentligetransport.dk/service/for-tourists/
Zone map of Greater Copenhagen: http://www.moviatrafik.dk/dinrejse/kort/zoneoversigt/Documents/Hovedstadsomraadet/1.pdf
On Rejseplanen (travel planner) you can plan your journey in Copenhagen or Denmark (choose English):
Sights
If you have the time to explore the city, there are several interesting sights and museums in and around Copenhagen.
A few suggestions in the city centre:

- The National Museum of Denmark
- Tivoli Gardens
- Rosenborg Castle
- Ny Carlsberg Glyptotek
- National Gallery of Denmark
- Nyhavn (New Harbour)
- Christianshavn
Suggestions for interesting destinations outside of the city (ask for ticket information at the Central Station):
- Frederiksborg Castle: Copenhagen-Hillerød, S-train from Nørreport or Vesterport
- Kronborg Castle & Maritime Museum of Denmark: Copenhagen-Helsingør, kystbanetog (regional train) from the Central Station or Nørreport
- Roskilde Cathedral and the royal tombs: Copenhagen-Roskilde, regional train from the Central Station or Nørreport
- Louisiana Museum of Modern Art: Copenhagen-Humlebæk, kystbanetog (regional train) from Central Station or Nørreport
For further inspiration see www.visitcopenhagen.com/copenhagen-tourist for Copenhagen and www.visitdenmark.com/denmark/tourist-frontpage for the rest of Denmark.
For restaurants see www.visitcopenhagen.com/copenhagen/gastronomy/restaurants.
If you have any particular interests or questions, please feel free to ask.