It's easy – and pleasant too - to walk or cycle in Amsterdam, while public transportation system includes excellent tram network, metro (subway) and canal bus boats.
The centre of Amsterdam, where most of the attractions, sights, entertainment and night-life is concentrated, is easily walkable. In fact, walking round Amsterdam, with its picturesque water-side streets lined with traditional canal houses, is one of the greatest pleasures of Amsterdam and an attraction in itself.
You can also do as many locals do and cycle: bike hire places are widely available and designated cycle lanes are everywhere. Expect to pay around 4 euro an hour, 10 euro a day or 30-40 euro per week (cash deposit or/and passport are required to hire a bike). Get a good lock, though, as theft can be a real problem.
Amsterdam is flat, and cycling is easy (although the humpback canal bridges will require a bit of a push if you are not fit and your bike isn't equipped with many gears).
The canals that criss-cross Amsterdam provide excellent opportunity for water transport and there are several companies offering sightseeing cruises as well as a regular canal-bus boats. The Canal Bus operate three colour-coded lines that give easy access to all major sights and provide fantastic opportunity to see Amsterdam from the water level. A day ticket for all the lines cost 20 euro and allows for unlimited use of the network for 24 hours (so if you start at midday you have until midday the next day). If you buy two days, the second one is half price.
The main stop is opposite the central station, but you can get tickets at Rijksmuseum, Leidseplein and Anne Frank House stops as well as at many hotels, Amsterdam Tourist Information Offices. If you just want to hop onto the boat and have no time to get a ticket, you might be able to persuade the skipper to let you on to nip out at one of the main stops to buy your ticket there. Get a map and the timetable to make a full use of this excellent service.
An alternative is a Museum Boat run by a company called Lovers, which has two lines which stop at slightly different locations (the price is the same) and offers discounts on entry to several of the major museums (these have to be pre purchased with a ticket, so planning is needed).
Obviously, the canal boats are not the cheapest or fastest way to travel round Amsterdam, but an a very pleasant one, and at least one such a cruise (whether involving any hopping on and off or not) is a must for any visitor.
If your hotel is near a canal bus stop, the boat is actually a reasonable alternative to a taxi or more conventional public transport when travelling back to the train station (get your ticket the day before to get the full use out of it).
GBV runs the proper Amsterdam public transport system, comprising trams, buses, small metro and some ferries in the north part of the city. Centraal Station is the hub for all of those, and all are covered by the same ticket system: strippenkaart, a long thin cardboard ticket divided into strips. Fold the card over and validate each strip in one of the on-board machines.
One adult travelling for up to one hour within one zone (most of the central Amsterdam is covered by one central zone) costs 2 strips, extra zone is one strip more. Two or more people can use the same card, provided requisite number of strips is validated. You can change, as long as you remain within the zone and within the 1 hour timespan.
Tickets are available on trams and buses (at 1.60 per journey/zone/hour), but it's cheaper to buy longer cards (15 strips) in tobacconists and GBV offices. An unlimited day card for the whole network is around 6.50 euro.
Trams are the most useful in the centre (buses go mostly to the outlying districts, and so does the metro) and are very easy to use: there is a map of the line on-board each vehicle, the stops are announced by name by an automated voice system in the trams and there is a map of the whole network at each stop.
In my experience the tram and bus drivers are among the few people you might meet in Amsterdam who won't necessarily speak any (or very limited) English, so it's useful to learn how to pronounce your destination name in Dutch.
The Schiphol airport is connected to the city by frequent (every ten-twenty minutes on weekdays and every hour at night) trains.