Nearest Airports are Leipzig IATA: LEJ, Magdeburg-Cochstedt IATA: CSO, and Berlin IATA: TXL, SXF. Allow 90 minutes transfer from LEJ, 2,5 to 3 hours from the other airports using public transport.
The easiest way to get to Dessau is by car, using the motorway A9. It has three exits depending on where are you coming from. If you arriving from north use the exit "Dessau Ost" faster or "Vockerode" on a more scenic route. From the south the exit is "Dessau Süd".
There is also a possibility to arrive by train. Regional trains connect to Wittenberg 30 minutes, Leipzig 60 minutes, Halle 50 minutes, Köthen 20 minutes and Magdeburg 60 minutes on an hourly and Berlin 100 minutes on a 2-hourly basis. Exit at Dessau Hbf. Dessau main station. There are some more suburb stations, which are usually not relevant for visitors.