By car:
The island is car free. You can travel with your car to Norddeich-Mole or Norddeich Airport, where you can park your car. From there you can hop directly onto the ferry or an airplane to the island.
By Train:
Directly by the harbour Norddeich-Mole is the train station, where long distance and also regional trains arrive daily.
By ferry:
The ferry connections to Juist are tide dependent, which is why usually there's only one ferry per day, which travel for about 1,5h. You can also travel to Juist by speedboat. more information you will find on frisonaut.de
By Plane:
The Frisia Airplanes need about 5 minutes to the island. The airport is a little bit outside of Norddeich so plan a little bit longer to get there. The airfield Juist is also not located in the Centre, you can catch a carriage to the island centre wich is about a 1h journey.