The Spreewald is easily reached from Berlin by regional train. Services on the RE2 line run from Berlin Ostbahnhof and Berlin Hauptbahnhof to Lübben (around 55 minutes) and Lübbenau (around 70 minutes), with trains roughly every hour. No reservation needed — a Brandenburg day ticket covers the journey.
By car, take the A13 motorway south from Berlin and exit at Lübben or Lübbenau. The drive takes about an hour from the city centre.