By train or by bus from Vilnius. It takes about 30 to 45 minutes. Tickets for the bus can be purchased at the bus station in Vilnius and cost about 5,60 Litas (one way).
The town is small enough for everything to be reached on foot, but there are also buses running from the bus station (where the buses from Vilnius also arrive/depart) to the castle.
Trakai Castle Museum, Kęstučio str. 4, ☎ +370 528 53 941 (firstname.lastname@example.org), . 10:00-19:00. Reconstructed residence of Lithuanian dukes in 14th century. Most famous castle in Lithuania, probably symbol of medieval Lithuania itself. Many concerts and plays during summer season.14 LTL.