The nearest airport is Schiphol (Amsterdam Airport). A direct connection by train to "Amsterdam Centraal Station" will get you in the center of Amsterdam in 15 minutes. From there you can take the tram (number 1, 2, 5), get off at "Koningsplein".
The nearest station to the library building is "Amsterdam Centraal station". From there you can take the tram (number 1, 2, 5), get off at "Koningsplein".
You can walk to the Amsterdam University Library from the central station within about 25 minutes. Trams (1,2 and 5) leave from "Amsterdam Centraal Station" to stop "Koningsplein" at two minutes walk from the library. Plenty of tourist attractions are in close vicinity of the venue and are reachable by foot.