Copenhagen's public transport system is amongst the most efficient and reliable in the world, constantly being developed and improved. Public transport will get you anywhere you wish to go in the city and the suburbs.
The Greater Copenhagen area is divided into zones. At bus stops and stations, you will find coloured zone maps by which you can calculate the fare for your journey. The number of zones you pass through on your journey from A to B determines the fare you have to pay. You pay for a minimum of two zones.
Metro, bus and train can be combined as much as you like as long as your ticket is valid, as shown on its back. You can buy your ticket at the ticket office, using the machines inside the stations or, if you are taking the bus, directly from the driver, but bring coins, not notes. If you are going to be using the public transports a lot, you might want to consider buying 10 trips at one time, a 24-hour-ticket or a Copenhagen Card, which will also give you free access to 60 major attractions and various discounts.