Here there is an official DESY page with information on how to reach DESY: https://www.desy.de/about_desy/getting_there/hamburg/index_eng.html
Be aware that you are not able to buy tickets in buses, so you either buy them at a train/metro station, or you can use one of the HVV app: https://www.hvv.de/en/service/hvv-apps
If you arrive at Altona train station, you can do S-bahn 1 in the direction of Wedel/Balnkenese and change to bus 1 on the Ottmarschen, or you can take bus 1 directly at the train station (it will be a ~5-7 longer ride, as S-bahn+bus)
If you arrive at the airport, you can also use shared taxi MOIA, which drives you directly to the DESY https://www.moia.io/de-DE/mitfahren/app
