From the airport
Take the S-Bahn to main-station and then ...
From the main-station
Take tram 17 (nightline N16) from Hauptbahnhof/main station (direction Amalienburgstr.) to Botanischer Garten, turn right into Franz-Schrank-Strasse (altogether around 15 mins). The Tram runs every 10 minutes during the day, every 20 minutes in the evenings. It is also a nightline (N16)!