Hamburg has a well developed public transport network with busses, rapid transit trains (S-Bahn), and sub-ways (U-Bahn). A specialty of Hamburg is that the subway runs mostly a lot above ground, while the rapid transit trains do tunnel underneath the city and only go above ground in the suburbs. Another specialty and highly recommended if you have some spare time are the HADAG passenger ferries running across and along the Elbe river, which you can use with your public transport ticket.
The airport and the main train stations are all connected to the rapid transit system.
To get around locally you may use the "Stadt Rad" system, a system of rental bikes (you may recognise them by their bright red colour). Stad Rad stations are scattered throughout the city. There is one station also on the DESY campus. You need a android or IOS app to book bikes. The first 30min are always free.
In the area surrounding DESY an on-demand shuttle service exists, which is closely integrated into the public transportation network. Again you need to install an app on your mobile phone (IOKI app) to book the shuttle. You may use the shuttle with a normal public transport ticket plus a small surcharge.
Of course the usual taxi service is available in Hamburg, which you book by phone or through several WEB services. At DESY the conference secretariat or the guard at the main gate will assist you to call a taxi.
The complete city area of Hamburg is covered by the shared ride service MOIA (MOIA shared ride service), where special electrically powered mini-busses offer door-to-door transport. Prices are in between the public transport and the taxt service.