The easiest way to get around is by S-train. For destinations between S-train stations or away from the main traffic channels you can take one of the local buses, most of which do not run as frequent as in the central part of the city.
There are taxi stands almost all S-train stations, but it will quite often be that no taxis are available and you will have to call one. Vest-Taxa +45 43 45 45 45 is usually the fastest in the western suburbs and Taxa Selandia +45 70 10 66 66 in the far southwestern suburbs. Taxa 4x35 +45 35 35 35 35 is a good option closest to the central part of the city, but further away some waiting time can be expected.
