No matter which transport you use, the two closest hubs are Berlin and Leipzig/Halle. If you aren't in the vicinity yet, you will likely pass through one of them.
By plane
Berlin Tegel IATA: TXL, Berlin Schönefeld IATA: SXF and Leipzig/Halle IATA: LEJ are the closest airports. Of these three, Berlin Tegel currently offers the widest range of international options.
By train
Hourly ICE trains on the Leipzig-Berlin line stop in Wittenberg in both directions. The ride takes 40 minutes from Leipzig Hbf or 45 from Berlin Hbf. As a slower but cheaper option you can also use RE trains, which also run about hourly. The ride takes 1h15m from Berlin, 1h05m from Leipzig, or one hour from Halle.
By car
The A9/E51 motorway passes west of Wittenberg. Use one of the exits Klein Marzehns, Köselitz or Coswig Anhalt. The town lies at the crossing of the main roads B2 and B187.