By train
Hamburg has five major stations: Hauptbahnhof central station, Altona, Dammtor, Harburg, Bergedorf. Various types of train service are available.
ICE Inter City Express high speed train service to or from most major German cities, including Berlin, Cologne Köln, Dusseldorf, Frankfurt, Munich also to Basel and Zurich Zürich Switzerland. There are usually hourly service to most destinations during the daytime.
Direct service to or from Copenhagen and Aarhus Denmark, Budapest Hungary, Prague Czech Republic, Vienna Austria, and Bratislava Slovakia.
Use the German railway's online trip planner (http://reiseauskunft.bahn...) to find connections to/from Hamburg and buy tickets.
Hitchhike
You can leave Hamburg to the south A7-Hannover/Frankfurt/Munich and southwest A1-Bremen/Cologne/Netherlands from the filling station known as "HH-Stillhorn" you can get there with the number 13 bus from suburbanstation S-Wilhelmsburg.
To Berlin you can start at the "Horner-Kreisel" and take the number 161 bus from S-Berliner Tor or walk from U3-Rauhes Haus.
You can find cars (http://www.mitfahrgelegen...) driving to most German cities for €10-20.
From the UK, it may be an idea to take a ferry to Denmark and then hitch down rather than going via Holland.
By bus
Buses serving other cities regional, national, and European destinations arrive at or depart from Hamburg's central bus station "ZOB" (http://www.zob-hamburg.de/), which is located near the central railway station Hauptbahnhof two minute walk. Destinations include Berlin several times a day.
Buses to Lübeck depart from Wandsbek.
Buses to Bosnia are eg. run by Salinea, (http://www.salinea.net/re...)
By car
via the Autobahn:
A1 to/from Lübeck north-east — To get to the city change to the A24 at "Autobahnkreuz Ost".
A1 to/from Bremen, Cologne Köln south/south-west — To get to the city change to A255.
A7 to/from Flensburg, Kiel north — To get to the city exit at "Bahrenfeld".
A7 to/from Hanover, Kassel south— To get to the city exit right after the "Elbtunnel" at "Othmarschen" or "Bahrenfeld". Use the rightmost pipe of the "Elbtunnel" to exit at "Othmarschen".
A23 to/from Husum.
A24 to/from Berlin.
Be prepared to pay for parking. Hamburg has a wide selection of P+R Park+Ride parking areas outside the city centre, where you can park for free and very easily use public transport to get into the city.