Amsterdam's main train station is Centraal, which has regular and efficient connections throughout the country and to all neighbouring countries. There are train-ferry services to Britain, or you can catch the Eurostar train through the Chunnel. Eurail passes are valid in The Netherlands. The Netherlands are very amenable to cycling - this is one of the flattest places in the world, and there are dedicated bike paths throughout the country. Bikes are allowed on trains for a nominal charge and on ferries for very little if any charge.
Ferries run between Amsterdam and Britain and Amsterdam and Norway.
Trains also connect the airport to stations throughout the country. Free shuttle buses run to many of they city's big hotels. You can get around lots of Amsterdam on foot. Public transport is very good - its hub is Centraal Station, where tram, bus and metro lines converge. You can get a free map of central-area public transport at the station.