There is really only one true way to experience Amsterdam, or any Dutch city in fact. One must join the throngs of bicyclers!

The Netherlands is truly remarkable in how well integrated bicycle transportation is into the general societal culture. Biking paths can be found in urban and rural areas alike, with bike specific traffic signs to help bicyclers find their way from Village A to Village B. The country even has bike specific traffic lights. I don’t have a picture of one of these traffic lights, but click here if you want to see for yourself. It certainly helps that the country is very flat, making a bicycle ride a much more endurable experience! In addition, bicycling in a city with proper bike lanes and explicitly outlined (and followed!) rules for bike/car/pedestrian relationships makes for a much safer and more pleasant bicycle ride.
But I must emphasize how very important it is to know and follow Dutch bicycle rules. If not, you are likely to annoy and frustrate those biking around you (not that I am speaking from experience, of course!). The busier intersections can be bewildering to navigate to the inexperienced Dutch city bicycler. And afternoon rush hour on bike can feel just as busy as it does when traveling home by car on a highway. You definitely have to be prepared and ready to go as soon as that bike traffic light turns green to avoid being run over by those behind you! However, these technical details can be quickly learned and you are soon navigating around town with ease. Biking really is a great way to experience a city. Viewing the sights and mingling with the locals is considerably better when doing it from a bicycle seat rather than from behind a car window.
About to start our day, after picking up our rental bikes and planning our cycling route.
During our afternoon picnic and nap at VondelPark
There are bicycles everywhere in Dutch cities and villages. This picture was taken when Jonathan and I visited Amsterdam in December, 2004. Yes indeed…that is a multi-tiered bike parking garage! It is located just outside of the central train station. 
For the more interested reader who is curious about the wide use of bicycles (to carry cargo, to transport children, to give a friend a lift), you can check out Amsterdam Bicycles - 1 Street Corner; 82 Bikes; 73 Minutes. Being initiated into the Dutch cycling scene by a Dutch husband and my Dutch family, I find the writer and photographer’s commentary to be humorous at his total disbelief at how Dutch utilize their bicycles. But at the same time, being a fellow American, I can relate with his amazement.
And this short video is another way to experience the Amsterdam bicycling scene. Enjoy!