Copenhagen tickets and the zone system
In Copenhagen, public transportation operates on a zone system. The minimum ticket is the two-zone ticket and can be purchased from ticket offices, vending machines and bus drivers. This allows you to travel around Copenhagen in two zones: Starting at the zone where you purchased your ticket, plus one adjoining zone - for an hour. You are allowed to switch between trains, metro and buses within that hour, as long as you board before the hour/min on your ticket have expired. For additional help, you can always ask a local as the zone system can be a bit complicated for first-time visitors.
As a tourist in Copenhagen, you should always check how many zones you need. The map is displayed at stations and distances are color coded, this makes the system easy to use. There is no exception for tourist in Copenhagen when it comes to ticket inspection. The same rules apply both to locals and to tourists - even if you misunderstand how the system works.
A cheap alternative is the Copenhagen Card, which gives you free public transportation throughout the region and free admission to museums and sights.
Copenhagen by S-Tog
The S-train service is the powerhouse of the city's municipal transit system and this is similar to the German networks. The distinctive red trains are always clean, modern, and equipped with free WiFi. The S-train runs from early morning to late night. On the weekends, the trains run once an hour at night apart from the F-line which runs twice an hour at night and other lines are extended. Announcements regarding the S-trains are in Danish only.
Copenhagen by metro
The metro in Copenhagen runs from Vanlose through the city centre and branches to Orestad and the airport. There is no set timetable for the metro and it runs non-stop at night in 15-minute intervals. The metro runs automatically and there are no drivers, so the doors close automatically.
If you want to save money on getting around in Copenhagen, here's a secret: Every first Sunday of the month all rides with the city trains are free - not including the metro and buses.