In Amsterdam, more then anything, walk around. Museums that I recommend: Van Gogh Museum (if you like Van Gogh and/or modenr art), Rijksmuseum (if you like 17th century art) and the Anne Frank House. For the latter you really want to make reservations well ahead through the museum's web site http://www.http://www.annefrank.org. Otherwise you may wait for an hour or more to get in. Reservations for the Van Gogh are also recomendable. The Rijksmuseum doesn't normally have waiting lines.
Amsterdam is a relatively small and compact city, so for most people 1 or 2 days in the city itself are enough. You may consider an excursion. There are many destinations closeby, cities such as The Hague, Rotterdam and Utrecht, and seeing some of the countryside is also very interesting, especially the lowlands surrounding Amsterdam.
For more information, see:
http://travellr.com/questions/netherlands/16503/3-days-in-amsterdam-what-to-seedo over 4 years ago