Getting Around - The best way to get around the city is through metro. The city is very well connected, the metro departs in every few minutes and are very prompt. There are three lines M1, M2 and M3 and a total of 37 stations spread across 35.9 kms operating 24 hours a day. Most of the attractions are easily accessible by metro.
It is advisable to buy a city pass which is valid on buses, trains and metro travel. These tickets are available as per the zones you would want to travel. Ensure to check the map before purchasing them. If you wouldn't want to worry about the zones and travel freely, checkout the Copenhagen card. You can travel freely in zone 1-99 (metropolitan area) by bus, train and metro. With the ticket you also get free access or discount to a number of museums and attractions in Copenhagen and the surrounding area.
Another way of exploring the city is by renting a bike. For all the adventurers and the adrenaline junkies out there pick up a by-cycle and off you go. There are several companies that provide bikes on rent and travelling around in pretty easy too. The cycle paths are quite extensive and there are separate lanes which are not shared with cars or pedestrians. Always keep to your right, ensure you follow traffic rules and if you are a first timer, be ready for a few unpleasant stares from the passers-by.
Places to visit - To be very honest, it will easily take more than a day to explore this place. But if that is all you have, here are some must see places that can be covered in a day.