While Amsterdam is officially the capital of the Netherlands, much of the paper-pushing and office stuff is located down in the Hague (Den Haag). Trains go several times per hour from Amsterdam Centraal to Den Haag Centraal and the journey takes about 50 minutes and costs just under €10 each way for adults.
The Embassy is about a 10-minute walk from Den Haag Centraal, and directions and loads of other information is available on the offical Embassy website.
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Lange Voorhout 102?
2514 EJ The Hague ?
Phone +31 70 310-2209?
Fax: +31 70 361-4688
Official US Embassy in the Netherlands website
American Citizen Services
Things like passport services, notary services, and reporting births of American citizens etc. are taken care of at the American Consulate in Amsterdam. They are located just behind the Rijksmuseum, or south of the museum if you are looking at a map.