You can't - there are none. In fact, there are no official post offices to be found in any Dutch city since October 2011, when the last post office closed in Utrecht, a major city south of Amsterdam.
But that doesn't mean that there are no postal services. From 2008 to 2011, the traditional post offices were replaced with "service points" where customers can purchase stamps, send letters and parcels, and other typical postal services. These operate just like their predecessors, but are located in newsstands, tobacco shops, supermarkets and other stores. What's more, there are 2,600 of them, as opposed to the previous 250 post offices. Shops that offer postal services are clearly marked with the acronym TNT - Thomas Nationwide Transport. (TNT started out as an Australian transportation company before it was acquired by Dutch telecommunications company KPN, who kept the name.)
In 2011, TNT turned its postal services over to an independent company, PostNL. While the name "TNT" is still emblazoned on service points across the country, perhaps this will eventually be replaced by the new company name; check this article for any updates on the situation.
Below is a list of postal service points near several popular tourist attractions in Amsterdam. In addition, stamps are sold at many other sites (such as the Amsterdam Tourist Service opposite Central Station), and mailboxes are located all over the city.
TNT Post Service Points near Popular Tourist Attractions
- Ako (newsstand)
Open daily, 10 a.m. - 8 p.m. (Wed till 9 p.m.)
Close to the Bloemenmarkt (Flower Market) and Rembrandtplein
- Albert Heijn (supermarket)
Open Mon - Sat, 8 a.m. - 8 p.m. (Sat. till 6 p.m.) Closed Sun.
Close to the Rembrandt House Museum.
- Gebr. Winter (stationer)
Open Mon 10:30 a.m. - 6 p.m., Tues - Fri. 9 a.m. - 6 p.m., Sat 10 a.m. - 5 p.m. Closed Sun.
Close to the Anne Frank House, Westerkerk and the Homomonument.
- Kantoorboekhandel Brugman (stationer)
Alexander Boersstraat 25-C
Open Mon - Sat, 8 a.m. - 6 p.m. (Sat till 5 p.m.) Closed Sun.
Close to the Vondelpark and Museumplein; opposite the Stedelijk Museum
- The Read Shop (bookstore)
Marie Heinekenplein 28
Open Mon - Fri 9 a.m. - 5:30 p.m. Closed Sat and Sun.
Close to the Heineken Experience; opposite De Appel Arts Center.
- Spar (supermarket)
Open Mon - Sat 8:30 a.m. - 7 p.m. (Sat till 6 p.m.)
Close to ARCAM (Architecture Center Amsterdam), the Nederlands Scheepvaartmuseum (Dutch Maritime Museum), and Science Center NEMO.