The cheapest way, of course, is to walk. You can buy a Strippenkaart for about 5 euros with 8 strips on it, probably good for most of a day if you take the tram in the centre. Each trip in the centre, one zone, will use up two strips and is good for about an hour or so, so you can take another tram or metro within that hour on the same ticket.
Another cheap way is to use the Stop/Go bus. This mini-bus seats about 15 people and takes a route starting by the Public Library next to Nemo on the waterfront near Centraal Station and, with a stop at the station, then follows the Prinsengracht canal all the way around to Waterlooplein. You can hail the bus or ask the driver to stop anywhere along the route. Tickets from the driver cost 1 euro (cheaper than a ticket on the tram) and are good for an hour. You can get to most of the popular attractions from this route, within a short walk. You can also use the Strippenkaart and the driver will stamp one zone (two strips) for you. They run every day between 9 and 5:30 about every 12 minutes.