Below are given some general information about the connections from each airport, but: To find the best connection from your airport to Magdeburg, you should check the
internet page of the German Railways (Deutsche Bahn AG),
which provides detailed information about train connections in Germany (and surrounding countries).
When checking the schedule, try to minimize the number of transfers (changes) and look at the total travel time (duration) which is given. Also the one way fare for each connection will be indicated. The webpage gives you (at least) three connections. Then you may add some earlier or later connections. The first page gives you just the time of departure and time of arrival as well as the number of transfers. You may then go to the page "itinerary" which offers more details on the transfers.
The trains marked IC (Intercity) or EC (Eurocity) require a supplement of EUR 3.60. The fast ICE (Intercity Express) trains, recommended especially when you go through Frankfurt(Main), have a special fare. The fares indicated on the internet page of the German Railways will already include these extras.
From the airport Berlin-Tegel, there is a frequent bus service X9 to Berlin's main train station Zoologischer Garten ("Bahnhof Zoo"). It takes about 20 minutes.
From the airport Berlin-Schönefeld there are trains every 30 minutes to Zoologischer Garten. They take about 20 minutes. There are various other connections from Berlin-Schönefeld to Magdeburg that you may find.
From Zoologischer Garten there are direct connections to Magdeburg which take about 90 minutes. There may be some connections via Stendal, which may be a detour.
From Frankfurt Airport it takes about 4 hours by train. Note that the airport has two train stations and make sure that you go to the right one for your connection. You take a train to Frankfurt(Main) Hauptbahnhof. From there one has two direct trains and many with a convenient transfer in Braunschweig. Depending on the time of day, you may wish to take another connection, but make sure that a later connection does not get you to Magdeburg faster.
When checking the train schedule make sure that you are NOT looking at Franfurt(Oder) which is east of Berlin. Also be careful that you do not run into a direct connection that makes a huge detour, is more expensive and takes 7 hours.
From Hannover airport there are a direct bus and the S-Bahn (suburban train, Line 5) going to Hannover Hauptbahnhof. It takes about 20--30 minutes. Most connections are direct, a few require a transfer in Braunschweig (or -- with a small detour -- in Stendal). The travel time is about 90 minutes.
From the airport Halle/Leipzig take bus line 300 directly to Halle Hauptbahnhof, 25 minutes of travel time. You could also take bus line AIR to Leipzig Hauptbahnhof, 20 minutes of travel time, but this may be a detour.
From Halle it is about 60 minutes, depending on the train. All connections are direct.
Further questions? Ask via e-mail at stoch2002@uni-magdeburg.de.