Amsterdam is the best city in Europe for a bicycle. There are so many bicyclists that they comprise the majority of people moving around. The next largest group is people walking. These people could be locals, in which case they will be looking out for bicycles. The problem with biking in Amsterdam is the tourists who walk across the bike lanes without looking for bicycles.
Where I grew up, there were sidewalks and roads. Mostly, bikes ride on the right edge of the road, perhaps in a specially painted bike lane. If there were any separate bike lanes, the would be on a path going through a wooded area, or college campus. In most cases this separate bike lanes would be shared by walkers, joggers, rollerbladers, bikes and skateboarders.
In Amsterdam bikes get a special lanes all to themselves. If you are on foot and walking in this lane you should always get out of the way of any bicycle coming towards you. There are 3 "lanes of traffic": the sidewalk, the road, and the special bike lane in between which is separated from the sidewalk and road by 2-3" cobblestone medians.
So when crossing the street, a tourist may see this bike lane and simply think it is another sidewalk. I have nearly been hit by a bike this way only once. As a bicycist, I took my mountain bike to Holland with me; it's a good thing it has good brakes, and I never hit anyone.
If you are into riding bicycles and are in reasonable shape, you may find that you ride much faster than the Dutch people. There are two reasons for this: first the Dutch are not usually in a big hurry like Americans, and second their bikes are pieces of crap by our standards.
Holland is a flat country, so 27-speed bikes are not ever needed. Furthermore, the Dutch don't typically have the equivalent of $1000 to shell out for a bike like we do. Last, because there is a serious bike theft problem in Amsterdam, even those who have the money will rarely spend it.
You can rent a Dutch bike at various locations throughout the city. Standard Dutch bikes may remind you of something you parents rode as kids in the 50's. You sit upright, only have 3-4 speeds if any, and slowly pedal your way across the extremely flat county. The average Dutch bike must weigh about 50 pounds, so if you take out a standard rental don't expect to do too many BMX tricks. Perhaps the bikes are so heavy so they can better push through the heavy winds you will encounter in the countryside. Not.
When I took my bike with me, I rode in Amsterdam many times. That was educational, dangerous, and interesting. One of the charms of Amsterdam is that it's such a small place compared to Paris, London or Rome. You can get anywhere in Amsterdam's city center within 15 minutes.
To the south of Amsterdam is the Amsterdamse Bos (Amsterdam Forest). This man-made forest is a product of the post-Depression era in the Netherlands. The Amsterdamse Bos is a wonderful, idyllic place to ride shorter distances. You have to ride south out of Amsterdam past the RAI to get there.
Another time I rode to Durgerdam and back. This was fun, but my Dutch friend I was riding with wanted to stop for beer every 15 minutes or so. Beer and riding don't go together for me, so I hurried him along.
My crowning acheivement on a bicycle was to ride up and down the island of Texel, north of Den Helder between the North Sea and the Waddenzee. I bought my train ticket (one for me and one for the bike, don't forget!) to Den Helder, and rode tothe ferry landing. After a 20 minute ferry ride we arrived at the island.
I rode 80km that day, half in the wind and half out of it. I learned a big lesson that day. When I rode north, I stayed behind the western dike and safely out of the wind. This is the most interesting part of the island, with forests, dunes, a few tourist attractions, and miles of memorable paths to ride on as you head to de Cocksdorp at the northern tip of Texel.
De Cocksdorp has a nice lighthouse, and the town is quaint like the rest of the island. I still had my lesson coming, though.
As I began to ride south down the middle of the island, I no longer had the protection of the dyke to keep the wind off me. I learned that I would rather ride up the steepest hill in California than ride into the Dutch wind. The only relief along the central route was the few farms with huge windbreaks planted of cypress. I would catch my breath as I rode past the hedges, only to dread that point 100 feet ahead where the protection stops and the punishing winds start again.