Hamburg has three major train stations (Hauptbahnhof main station on Kirchenallee, Altona on Präsident-Krahn-Straße and Dammtor on Edmund-Siemers-Allee) so be sure to know where to board and exit the train.
Deutsche Bahn (DB) operates InterCityExpress (ICE), EuroCity (EC) and InterCity (IC) trains to and from Hamburg. If a seat is a must, make sure to make a reservation in advance - especially at weekends. If you do not have time to purchase your ticket beforehand in one of the stations, you can do so on the train at a small surcharge. However, make sure to find the DB ticket person quickly so they do not think you are trying to get a free ride. DB's website www.bahn.de is in English and fantastic, allowing online ticket purchases with credit cards.
The main station is fully loaded with a food court, supermarkets, bookstores, drugstores, a pharmacy and other small shops.