Every-one uses them, not just the old, not just the young, not just the poor, not just the rich; and with a city as flat, structured, and small as Amsterdam it's hardly a surprise.
As a tourist you won't necessarily feel the need that the locals have for the national form of transport, after all strolls along the canals and taking your time getting places is all a part of the holiday ambience. However, there are roughly three quarters of a million inhabitants of Amsterdam, and between them they own more or less 600,000 bikes, so surely they must be on to something, and as they say; when in Amsterdam.
Whether the city has adapted to the cyclists or the cyclists have adapted to the city is unclear but which ever is the case the city is incredibly bicycle friendly with bike stands all over the place for leaving your bike safely, and bike lanes on all the newer roads. The city centre, due its narrow streets is a little less friendly and cyclists will often find themselves careering down old roads neck to neck with cars this is something to watch out for. Another point to watch out for that separates the tourists from the locals is the tram lines. If you were to get your tires stuck in the tram lines you would not be the first but you would certainly mark your self out as a visitor: Always cross the tram lines at right angles!
You can rent bikes at various locations around the city but the best bet is at the stations where you can get a bike for around 12 Euros per day and up. It is highly recommended to do so at least for one day and to cycle out into the nearby countryside or along the Amstel River. Take a packed lunch with you and you won't regret it.
Many people choose to take biking into account when picking their holiday accommodation. With over 400 hotels in Amsterdam there are plenty to pick from but one might consider choosing a hotel a little way out of the city. Price wise it makes little difference if you are right in the city or a little way out; you should expect to pay around 60 euros to 140 euros for a three star hotel. However, if you do venture just a half hour's bike ride out of the city you will find holiday villages and guest houses which often provide a much more Dutch experience where you are more likely to meet Dutch people and sample what a Dutch holiday is like. Furthermore, with an out of town holiday option you can spend a few days exploring the beautiful stretched out Dutch countryside, whilst of course having the city a mere half hour's ride away; it's really the best of both worlds.