If you're flying directly to Bremen, chances are you either live abroad or are getting a connecting flight (either KLM through Amsterdam or Lufthansa through any number of other German hubs) - direct flights from the UK are thin on the ground, although Ryanair run services from Liverpool and London Stansted.
The airport is located south of the main city centre, and is well connected with the city though public transport. Trams leave the airport every 5-10 minutes during the week (less frequent on Sundays) and take around 10-12 minutes to reach the city centre for only a couple of Euros. There are also bus connections with Hamburg Airport through Bus2Fly.
By Train
Bremen is well connected throughout the rest of Germany through the rail network. The train station is located to the north of the city centre and is walking distance from its many attractions, bars and restaurants.
There are regular services linking Bremen to most major German cities - for full details of timetables and prices check out the excellent and ruthlessly efficient German railways site Bahn.de.
If you are connecting through a city outside of Germany, don't worry - Bahn.de has full listings for services across Europe. Also, if you're looking to make the whole journey by rail (Eurostar and all that) then check out the excellent Seat61.com. What that man doesn't know about train journeys isn't worth knowing.
