The "beach train" is not a train on rails but a motor vehicle in the shape of a train. It runs along the beach promenad, starting at the Western end of the beach in Duhnen and ending at Alte Liebe in the port, with several stops along the way. It runs right on the beach promenade. If you can't or don't want to walk long distances, this "train" is a fun alternative to experience the beach landscapes and the views of the sea, tidelands and the Elbe.
There are only four rides per day, so check the timetable in advance and plan accordingly. The fare isn't cheap - 5.50 € for the full distance. You can buy tickets on the spot from the driver.
Timetable and fares here
Buses are the way to move between the various districts of Cuxhaven if you don't have your own transportation, i.e. at least a bicycle. Bus connections are sufficient to get around but not really convenient for getting around in a relaxed way. Each bus line runs only once per hour. To Döse and Duhnen there are three lines from the centre, which means a bus every 20 minutes. The central hub is the train station where most lines meet.
Connections are not on big-city level but the fares are. The centre and Döse/Duhnen count as two different zones, and a single ticket is 2.30 € - the same as here in Karlsruhe. BahnCard holders get a discount. The Niedersachsen-Ticket, however, is NOT valid.
For longer stays, there is a multi-ticket for six rides (11.10 € for 2 zones), and there are also weekly tickets.
Tickets must be bought from the driver, and presented to the driver if you change or have a pass. There are no validators on the bus - the driver will stamp the multi-ticket by hand every time. No wonder the buses are often delayed.
From Cuxhaven the boats leave to the Red Rock in the North Sea calles Helgoland (see my Helgoland-page too under Schlesswick-Holstein). This is a must see from Cuxhaven, but falls in another German "Bundesland" (state / province), however I have to mention the place from where you best can reach this unique rock in the sea.