Some say the fastest and most flexible way of seeing Copenhagen is on a bike. Forty percent of Copenhageners use their bike everyday and the city has been designed to cater for cyclists with separate bicycle lanes on most larger roads. Cyclists are often allowed to ride both ways in one-way streets. If you are not used to biking in a busy city, be very careful in Copenhagen particularly in peak period as the locals ride fast and leave little room for leeway. Don't expect to get a warning when someone wants to overtake you. Always keep to the right and look behind you before you overtake someone — otherwise you could cause some nasty accidents.
In the center of the city, you can get around by the free public city-bikes. These are specially painted by various sponsors and are very simple bikes that you can find on special stands near major places like the main train station, Tivoli Park, the port and numerous other racks throughout the central city. After you insert a 20 Kr coin, akin to the system used for some shopping or airport trolleys, you can take the bike anywhere you want as long as you stay in the inner part of the city marked on the map on the bike. If you are caught outside these borders, you could be faced with a fine (around 1,000 Kr). When you return the bike to some stand again (not necessarily the same one), you will get your money back.
A word of warning though! Don't take away city-bikes that you see somewhere that are not on a stand. There are high chances that somebody will soon return for it and by taking it away you not only deprive them of their transport, but also their money. You will be very unpopular if the user arise while you are getting ready to leave. During the winter you will not find (m)any bikes, as they are being repaired in the local prisons as part of community service.
As an alternative to the city bikes you can rent a bike and these are far more comfortable. You can find a little bike rental shop called CPH bike rental on a side-street to Nansensgade on Turesensgade 10, five minutes from Norreport station. They rent bikes on a daily basis and use the proceeds to finance the shipment of used bikes to Africa. They also arrange city tours and sell picnic baskets. Their prices start at 60 Kr for six hours bike rent. Another bicycle shop is at the Central Railroad Station, where prices start at 75 Kr a day/340 a week.