Trams are one of the greatest hazards known to the new arrival in Amsterdam. Having navigated your way across a canal, four lanes of cars and a bicycle lane - trams are then prone to appear from nowhere and WHAM! - BE WARNED!!
The danger apart, trams offer a very extensive and cheap service. A free route map and English language guide are available from the GVB office outside Centraal Station. The cheapest ticket option is a strippenkaart, which are valid across the Netherlands. It works on a zone by zone basis - you punch out two strips for travel across one zone, three strips for two zones and so on. Dagkaarts (day tickets) are also available, giving unlimited use of trams during the day(s) of your choice. Tickets are checked at most times of the day and night so trying to avoid paying (being a zwartrijder - black rider) is not advisable.
